Warm the Whole Milk to about 95–105°F (35–40°C) and stir in the Instant Yeast with 1 tablespoon of the Granulated Sugar; let sit 5–10 minutes until foamy.
In a large bowl combine the Bread Flour with the remaining Granulated Sugar and the Fine Salt.
Beat the Eggs lightly and add them to the flour mixture along with the milk-yeast mixture; mix until a shaggy dough forms.
Turn the dough out and knead by hand or with a stand mixer on medium speed until it becomes smooth and elastic (8–12 minutes).
Soften the Unsalted Butter to room temperature, cut into pieces, and gradually incorporate it into the dough, kneading until the dough is shiny, very elastic, and pulls away from the bowl.
Place the dough in a lightly oiled bowl, cover, and let rise in a warm place until doubled in size (about 1–2 hours). For deeper flavor, refrigerate overnight instead of a long room-temperature rise.
Gently deflate the dough, divide and shape into a loaf pan or individual rolls (or braid if you like). Arrange in the prepared pan(s).
Cover and proof the shaped dough until puffy and nearly doubled (45–90 minutes depending on temperature).
Whisk one Egg with a splash of Milk and brush the tops of the proofed brioche for a glossy, golden finish.
Bake at 350°F (175°C) for 25–35 minutes for a loaf (less for small rolls), until deeply golden and an instant-read thermometer reads about 190–200°F (88–93°C) in the center. Cool in the pan 10 minutes, then transfer to a rack to cool before slicing.
