brioche bread recipe

1/4 cup warm milk (110°F/45°C) - 2 1/4 teaspoons active dry yeast (1 packet) - 1/4 cup granulated sugar - 4 large eggs, room temperature - 3 1/2 cups all-purpose flour - 1 teaspoon salt - 1 cup unsalted butter, softened and cut into pieces - 1 egg, beaten (for egg wash)