Make the yeast mixture
Start off by making the yeast mixture. You’ll want to add 3/4 cup of warm milk (about 105 degrees Fahrenheit) to a large measuring cup along with 1 1/2 teaspoons of yeast and 1 tablespoon of granulated sugar.
Give it a quick whisk and let it sit for about 10 minutes or until it becomes frothy.
Add everything but the butter to the mixer
Now place the hook attachment onto a stand mixer and add 4 cups of all-purpose flour (spooned and leveled off with a knife), 1/4 cup granulated sugar, 1 teaspoon of salt, 3 large eggs, and the frothy yeast mixture. 
Start off by mixing on low speed. Once the flour begins to incorporate into the dough, pick up the speed to high. You will want to continue mixing the dough on high speed until it begins to take shape. So about 4-5 minutes.
Add softened butter
Now cut up 1/2 cup of softened unsalted butter into chunks and add them to the dough.
Continue mixing the dough on high speed for 5-10 more minutes or until the dough no longer sticks to the sides of the mixer bowl. It should have a smooth elastic texture by this point. Have patience with the dough, this step can take a while.
Place the dough into a greased bowl to proof
Now place the formed dough into a lightly greased bowl (I use olive oil). Cover the dough with a kitchen towel or plastic wrap and let it rise for about 1 hour or until it doubles in size. To speed this up, place in the oven on the “proof” setting.
Shape into 12 rolls and proof again
Now punch down the dough and divide it into 12 equal pieces. Shape each piece of dough into round balls. 
Place the brioche dough balls into a 9×13 inch deep baking dish and let them proof covered for another hour. They don’t necessarily need to double in size in this step.
Brush with egg wash and bake
Now make the egg wash by combining 1 egg with a teaspoon of water and brushing it over each dinner roll using a pastry brush.
Bake the brioche dinner rolls in the oven at 350 degrees Fahrenheit for about 25 minutes.
Enjoy
