I think Brioche make the perfect burger bun. They're surprisingly easy to make and they’re soft, light and flavorful, and don't overwhelm the burger. This recipe is to make 6 large buns.

Brioche is an enriched dough, which means a dough that has ingredients beyond flour, water, salt, and yeast. In this case milk instead of water, and then eggs, butter, and sugar. It can be challenging to make brioche dough by hand so recommend using a stand mixer with the dough hook.

265 grams of lukewarm whole milk
9 grams active dry yeast
30 grams sugar
1 large egg and 1 egg yolk
435 grams of all-purpose flour
10 grams kosher salt
50 grams softened unsalted butter

I want to bake the buns using some retained heat that’s around 375F, that’s 190C. It takes some practice to get it right. The more you use your oven the more familiar you will be with how it performs and how it manages heat. But not all ovens are the same, and they’re going to perform differently based on their construction and insulation.

If you find it challenging to get your wood oven to the correct retained heat temperature then it may be easier just to bake them in a conventional oven at 375F, that's 190C, for around 18 minutes, or until they are golden brown.