For example, lets say I want to make a boule with instant yeast. What would the difference be if I let it rise very quickly in a hot environment vs if I let it rise very slowly in a cold environment? I'm more referring to the first rise (not sure what the name of this is--bulk rise?) but the question still stands for the shaping rise phase (again, I dont know what the right name for this rise it) as long as you dont let it rise too much. Thanks!
Longer rises produce better flavor, and are easier to control. In my experience, fast rises can also produce a slack texture.
While there are other, minor effects too, the major effect is flavor.
Longer and colder fermentation results in more complex and matured flavor. Same reason why beers and other alcoholic beverages are stored at around 8-12°C for a long time before being sold.
I'm not sure about the exact biochemical reasons behind this (I'm sure evaporation/concentration plays a role), but we know it works and that's the most important.
First, I agree with the above comments. To get the best flavor, time (and patience) are needed.
The stage between the initial mixing of the dough and the dividing/shaping is generally referred to as the bulk fermentation. The stage after shaping until the dough is placed into the oven is the final proofing (or simply the proofing).
Another thing that can improve the flavor of a bread made with commercial yeast (such as instant dry yeast) is a preferment. If you look for a recipe with a poolish, you can make a bread using instant dry yeast, and the process during which the preferment develops will enhance the flavor of the bread.
Happy baking -- and stay safe and stay healthy.
Ted