Combine Wet Ingredients: Add the yeast mixture and eggs to the flour mixture. Mix on low speed until a dough forms.
Add Butter: Gradually add the softened butter, a few pieces at a time, mixing on medium speed until the butter is fully incorporated and the dough is smooth and elastic, about 10 minutes. The dough will be sticky.
Step 2: First Rise
Rise: Transfer the dough to a lightly greased bowl, cover with plastic wrap or a clean kitchen towel, and let it rise in a warm place for about 1-2 hours, or until it has doubled in size.
Step 3: Shape the Dough
Deflate Dough: Punch down the risen dough and turn it out onto a lightly floured surface.
Shape: Divide the dough into 12 equal pieces if making individual rolls, or shape it into a loaf if making a single large brioche. Place the shaped dough pieces into a greased loaf pan or a greased muffin tin for individual rolls.
Step 4: Second Rise
Second Rise: Cover the shaped dough with a kitchen towel and let it rise for another 30-45 minutes, or until it has puffed up.
Step 5: Bake the Brioche
Preheat Oven: Preheat your oven to 375°F (190°C).
Egg Wash: In a small bowl, whisk together the egg and water for the egg wash. Brush the tops of the risen brioche with the egg wash.
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