In my humble opinion that would be a Brioche bun. Please dispute that if you have a better idea. I find that most high end restaurants serve Brioche buns with hamburgers and pulled pork sandwiches. Most restaurants use a plain white bread hamburger bun like you buy at Safeway. This bun needs to be really special. It can't over power the hamburger patty that is intended to be the star of the dish.
But... It has to be pretty, tasty and able to hold together when a well cooked 1/2 pound hambuger patty leaks its juices onto the bum. It can have toppings such as sesame seeds or onions or whatever else will add flavor.
I'm going to start this study with Chef Jacob's basic Brioche dough because he has reduced the fat content to make it easier to handle for newbie's that aren't familiar with handling high fat doughs. The audience for this dough is a large BBQ website that has a following of 85% men that have NO baking experience. The recipe has to be in volume not weight. Most of these website members have never heard of a digital scale for cooking. I will publish this recipe with both volume and weight measurements but most will only understand cups, teaspoons and a pinch of this or that.
I'm going to mix up Chef Jacob's basic Brioche dough tonight and delay ferment it in the refigerator tonight so I can bake it tomorrow. From what I can find on the World Wide Web... A hamburger bun should be 80 grams when you portion the bulk dough. Chef Jacob says you should press it down after the final proofing so the oven spring doesn't allow it to rise to much which would distort your bun to patty ratio. I would greatly appreciate any input from anyone that has knowledge of hamburger buns...