Bread always cracks one side and gummy centre

Eggs are troublesome, an egg is not always the same as it's mate in the box. Eggs are a natural product and vary dramatically in size, your original recipe called for one egg which you increased to 2 despite the rest of the ingredients being increased by 1.5? With all that in mind it might be your problem? There will be others along with more experience than me but I'd begin just by weighing one cracked egg, then crack in a second, whisk and use 1.5 times your original weight. Perhaps use medium eggs if possible too.

Your big crack shows a big oven spring at the weakest point, this is not necessarily a bad thing and could be controlled by scoring but I think you could've maybe waited a little longer on your final prove. I'll let other, more expert baker's advise further.

I would suggest using only the egg yolks.  I might use the whites if I had a weaker flour but you have bread flour.  It can take it.  No need for extra protein.

I would also heat the water til it starts to boil, whisk in the powdered milk while hot, drop in the sugar and oil (or a nice plop of butter and if you have a clean orange around, grate half of it and toss that in)  and let it cool down a bit, when you can hold your finger in it, drop in the two cold egg yolks and whisk them in bit, then stir in the cooled Tangzhong.  Stir the bread flour and yeast together.  Make a well in the middle and pour the liquids in.  

If you find the dough too wet to knead it, let it rest covered for 30 minutes then turn out onto a floured board or table to knead lightly.  Usually just getting it folded over with a bench scraper around the edges is enough that you can start to work a light knead on the dough.  Use AP flour for your bench flour and light kneading.  Then plop it into a bold and cover to rise.

Now about the rest... I think you may have trapped some gas when folding the dough, try just spreading it out and  folding more from the outside edges in.  Be sure to degas the dough thoroughly.  Roll up tightly being careful not to tuck in any excess flour or air.  Brush off any flour while you roll.  The loaf needs to be covered while rising to keep the crust from drying out as it expands.   It also looks like it went too early into the oven.  Try waiting just a little bit longer.  I know, but it will hold up.  With the bread flour, it should be able to double in volume nicely.  

I might also raise the oven temp a tad to 375°F  The bottom of the loaf looks pale but it is hard to tell from the photo.  Try rearranging the oven so that more heat is directly under the loaf and less above it.

Mini   

photos, That is very tricky business!  I think if you can handle that, this loaf problem is easy peasy.  

It may be that the pan is now too small for the amount of dough you've made. The dough shouldn't fill the pan more than about two thirds full at first, and should rise to the point where the middle of the dome of dough is only about 1 inch above the rim of the pan (lift the pan to eye level and sight along it to see where the top of the dome is). I think perhaps the dough didn't proof enough before you put it in the oven, so the spring was too much and the middle didn't get cooked. Try a bigger pan or dividing the dough into two smaller pans.

Also, if you are going to roll up the dough (I usually do this too), it helps to score the top of the loaf before baking, otherwise it will spring at the point of least resistance which is along the edge of the pan, and it will unroll.

seems to have a rather spectacular rise, and seems to have a very particular kneading / fermenting / shaping method in all of the recipes that I've seen. 

I wonder whether the issue that you have might be a combination of under-fermented, and not strong enough shaping (as well as maybe too much dough).

I'd suggest that you try one of the popular versions from this site, either FloydM's http://www.thefreshloaf.com//node/32997/hokkaido-milk-bread-tangzhong or Txfarmer's http://www.thefreshloaf.com/node/23662/sourdough-hokkaido-milk-loaf-classic-shreddable-soft-bread and see whether that works better for you.

I think you might find that the intensive kneading instructions, timing, and the shaping instructions (particularly in how best to roll out the dough for the best rise) in TXfarmer's blog and her other blogs that she links to might be just what you need to help solve your current issues.

Good luck, and happy baking!

 Your recipe looked good to me, but did look much too big for my 5” x 9” loaf pans.  I have done very few enriched doughs, and even less with ADY, but thought I’d refigure your version to 480g flour, change out the sugar to maple syrup, and try it with both ADY and with a levain.  My taste preference is for whole grains, so I did a mix of 100g whole durum, 180g whole soft white wheat, and 200g whole hard red wheat.  I did go back to butter instead of olive oil for the levain version, just because I ran out of good olive oil!  Oh – and I accidentally ended up with 73% hydration instead of the 65%, since I wasn’t thinking about the water content of the egg when I calculated it.  There’s no reason not to stay around the 65%, and it would likely be far more manageable.

 The levain one is retarding in the fridge, but the ADY one came out pretty good (except that I over-fermented it – oops!).  I’ll do a separate post about it, but thought I’d let you know that the 480g of flour woks out perfectly with the 5” x 9” standard 2-lb loaf pan.  This does ferment incredibly fast (which is why mine went over), but kneading it to full window-pane and rolling out 4 separate pieces in to tight rolls seems to help with controlling the rise. 

 Thanks for the inspiration, and I hope that you’ll have better results from the smaller version of the recipe (if you are using the same size loaf pan).