1/3 cup warm whole milk
2 1/4 teaspoon active dry yeast
1 large egg
2 cups unbleached flour
1/3 cup sugar
1 1/2 teaspoons kosher salt
4 large eggs, lightly beaten at room temperature
1 1/2 cups flour
12 tablespoons unsalted butter, room temperature
Put the milk, yeast, egg, and 1 cup for the flour for the sponge in a mixing bowl. Mix together with a rubber spatula until blended. Sprinkle the remaining cup of flour over the sponge, set aside, and rest uncovered for 30-40 minutes.
To make the dough, add the salt, sugar, eggs, and 1 cup of flour to the sponge. Mix by hand, working the ingredients together. It will start as a sticky mess, but it will gradually become softer. Continue to knead for about 10 minutes by hand, sprinkling the remaining 1/2 cup flour in a little ways in.
Once all the flour in incorporated, turn the dough out onto a work surface. Divide the dough in half. Set one half to the side. With the other half, knead all of the butter in, mixing directly onto the work surface until it forms a smooth, shiny ball. Once the mixture is homogeneous, add in the other half of the dough and knead and mix more, mixing and picking up any butter from the work surface until you end up with a smooth, elastic ball of dough. This process should take about another 10 minutes of kneading.
Transfer the dough to a large, buttered bowl. Cover tightly with plastic wrap and let rise at room temperature until doubled (about 2 to 2 1/2 horus). Deflate the dough by placing your fingers under it, lifting a section of the dough, then letting it fall back into the bowl. Work your way around the circumference of the dough, lifting and releasing.
Cover the bowl tightly with plastic wrap once more and refrigerate the dough overnight, or at least for 4-6 hours.
When ready to bake, divide the dough into thirds. Divide each section into 6 equal pieces, and shape each ball on a lightly floured work surface. Place the balls side by side in a greased loaf pan so you have 3 short rows, each with 2 balls of dough. Repeat this process with the remaining two large balls of dough.
Cover the pans with plastic and allow the dough to rise at room temperature for 2 hours or until doubled in size.
Preheat the oven to 375F. Lightly brush each loaf with and egg wash (1 large egg beaten with 1 teaspoon water). Use the ends of a pair of scissors to snip a cross into the top of each ball of dough. Bake the brioche for 30 minutes, or until an instant read thermometer reads 200F.
Cool to room temperature before serving.