Eggs/Butter/Milk Effects

Hi All,

I'm on a soft roll/bun kick right now while quarantining, and just curious about what each of the above additions do to doughs, specifically.  I know that Eggs and Butter both work to tenderize the dough, while whole eggs also help contribute some added protein via the whites.  

But my question is what do each of these add on their own?  For instance, if were to make a dough with just butter, no eggs, what should I expect when compared to a dough with both?  And vice versa--a dough with just eggs, no butter?

And also, what does milk do specifically aside from providing a different flavor profile?  

I know that understanding specific effects helps in engineering what it is you're looking for, so I'm looking to understand the individual characteristics so I can have an intended goal.  

Thanks again all,

Mike