One day before baking:
• TO MAKE THE LIQUID LEVAIN: In a large storage container, combine the pastry flour and 130 grams (½ cup plus 2½ teaspoons) water and mix well. Cover tightly and let sit in a warm place until approximately tripled in bulk, 16 to 27 hours.
The day of baking:
• Set 200 grams (7 ounces) of the butter aside at room temperature to soften.
• In the bowl of a stand mixer fitted with the dough hook attachment, combine the liquid levain with 200 grams (¾ cup plus 1½ tablespoons) water, the eggs, sugar, yeast, and fine sea salt. Mix on low speed for 5 minutes. Raise the mixer speed to medium and mix for 4 minutes. Add the 200 grams (7 ounces) of softened butter and mix on medium speed for 5 minutes.
• Turn off the mixer and cover the bowl with a clean, dry towel. Let sit at 25°C/77°F for 30 minutes.
• TO LAMINATE THE DOUGH TO MAKE BRIOCHE FEUILLETÉE, IF DESIRED: On a lightly floured surface, use a rolling pin to shape the dough into a ½-inch-thick square. Stretch a large piece of plastic wrap on a flat work surface and place the remaining 300 grams (10.6 ounces) cold butter in the center. Cover the butter with a second layer of plastic wrap. Beat the butter with a rolling pin to flatten the butter. Use the rolling pin to roll the butter into a flat rectangle, as long as the dough on one side and half the size of the dough on the other. Unwrap the butter and place it on the dough in the center. Fold the ends of the dough over the butter so that they meet in a seam in the middle. Stretch the dough and fold again at the seam to make a double fold.
• Cover the dough (laminated or not) with plastic wrap and refrigerate for 45 minutes.
• Butter 36 brioche molds (for brioche feuilletée or brioche à tête) or 3 loaf pans.
• TO SHAPE THE DOUGH FOR BRIOCHE FEUILLETÉE, IF DESIRED: Use a rolling pin to flatten the dough into a rectangle ½ inch thick. Cut the rectangle into 2-inch-wide strips and roll the strips into spirals. Place the spirals in the buttered brioche molds with the coil showing at the top. Alternatively, shape the dough into brioche croissants or any shape appropriate to laminated dough.
• TO SHAPE THE DOUGH FOR LOAVES: Split the dough into 3 equal balls. Split each ball into 8 round balls and arrange them in the buttered loaf pans in 2 x 4-ball grids.
• TO MAKE THE EGG WASH: In a medium bowl, beat the whole eggs and egg yolk. Add the milk and a pinch of salt.
• Use a silicone basting brush to wash the tops of the dough with the egg wash.
• TO PROOF: Cover the brioche molds or loaf pans with a damp kitchen towel and let sit at 26°C/81°F until risen, 2 to 2½ hours.
• Preheat the oven to 180°C/355°F.
• Bake until golden brown, watching closely to prevent burning, for 20 to 25 minutes.
• Allow the brioche to cool in the molds or loaf pans for 5 minutes. Transfer to a wire rack and allow to cool to room temperature.