1In a bowl, combine warm milk (about 100-110°F), yeast, and sugar. Mix well and let rest for 5 minutes until foamy.
2Add 2.5 cups of all-purpose flour, 1 teaspoon of salt, and 2 eggs. Mix using a dough hook or wooden spoon until incorporated.
3Add 4 tablespoons of room temperature butter. Mix until the butter is fully incorporated.
4Once the dough is formed, place it in a bowl coated with oil, cover with plastic wrap, and let it proof on the counter for 1-1.5 hours or until doubled in size.
5Turn the proofed dough onto a floured surface and divide it into 4 equal parts.
6Shape each dough part into a ball, and place them on a baking sheet lined with parchment paper.
7Cover the dough balls with plastic wrap and let them proof for another 30 minutes.
8Make an egg wash (beaten egg) and brush it over the dough balls before baking.
9Bake the Brioche buns at 350°F for about 20 minutes.