Brioche Hamburger Buns

1/3 cup butter
3 T sugar
4 1/2 t instant yeast
1 egg
3 1/4 cups all-purpose flour
1 1/2 t salt
1 1/4 cups buttermilk or 1 1/4 cups milk with 1 1/4 T vinegar mixed in and set aside for 5 minutes

Egg Wash:
1 egg
1 t water

Combine 2 cups flour, the sugar, yeast in mixer bowl.
Heat buttermilk in microwave for 1 minute.  Stir and then cook for  20 second increments until very warm to touch but not too hot.
Add buttermilk to flour mixture.  Mix with dough hook until well combined.
Add egg and remaining 1 1/4 cups flour.  Mix.  Add small amounts of flour until dough cleans off of the side of the bowl.
Turn onto counter and knead by hand until smooth and touchable, not sticky.
Divide into 6 equal pieces and roll into 6 balls.
Place on parchment paper lined baking sheet.
Let rise until double in size.
Brush with egg wash, bake in preheated 400 degree oven for 12 to 15 minutes or until golden brown.
Let cool before cutting buns in half.