Make the biga: In a large bowl, combine 2 cups (312 g) bread flour, 1 cup (240 ml) warm water (100–110°F / 38–43°C), and ½ teaspoon instant or rapid-rise yeast. Stir with a wooden spoon until a uniform mass forms and no dry flour remains, about 1 minute. Cover tightly with plastic wrap and let stand at room temperature overnight (at least 8 hours and up to 24 hours).
Make the soaker: In a separate large bowl, combine 3 cups (468 g) whole-wheat flour, ½ cup (57 g) wheat germ, and 2 cups (480 ml) whole milk. Stir with a wooden spoon until a shaggy mass forms, about 1 minute. Cover tightly with plastic wrap and refrigerate overnight (at least 8 hours and up to 24 hours).
Assemble the dough: Tear the chilled soaker into roughly 1-inch pieces and place them in the bowl of a stand mixer fitted with the dough hook. Add the biga, ¼ cup (85 g) honey, 4 teaspoons table salt, 2 tablespoons instant or rapid-rise yeast, 6 tablespoons (unsalted) butter softened, and 2 tablespoons vegetable oil.
Mix and knead in the mixer: Mix on low speed until a cohesive mass begins to form, about 2 minutes. Increase mixer speed to medium and knead until the dough is smooth and elastic, 8 to 10 minutes. The dough will be very soft and slack.
Brief hand shaping and first rise: Turn the dough out onto a lightly floured work surface (use bread flour) and knead by hand one minute to form a ball. Transfer the dough to a large, lightly greased bowl, cover tightly with plastic wrap, and let rise at room temperature for 45 minutes.
Perform folds: Lightly flour your fingertips. Gently press down the center of the dough to deflate it. Holding an edge of the dough with your fingertips, lift the edge and fold it toward the middle. Rotate the bowl 90° and repeat. Continue until you have completed a total of 8 folds. Cover the bowl and allow the dough to rise at room temperature until doubled in volume, about 45 minutes.
Prepare for shaping and preheat oven: Adjust oven racks to the middle and lowest positions and place a baking stone on the middle rack. Preheat the oven to 400°F (200°C). Spray two 9×5-inch loaf pans with nonstick cooking spray. Place an empty (not glass) baking pan on the bottom rack to receive boiling water later.
Shape the loaves: Turn the dough out onto a well-floured work surface (bread flour) and divide into two equal pieces. Working with one piece at a time, pat it into an 8×17-inch rectangle with the short side facing you. Roll the dough toward you into a firm cylinder, keeping the roll taut by tucking the dough under itself as you go. Turn the loaf seam side up and pinch the seam closed, then place the loaf seam side down into a prepared loaf pan, pressing gently into the corners. Repeat with the second piece.
Final rise: Loosely cover the loaves with plastic wrap and let rise at room temperature until almost doubled and the tops rise about 1 inch above the edge of the pans, 60 to 90 minutes.
Add steam, slash, and bake: Bring 2 cups of water to a boil on the stove. Using a sharp serrated knife or single-edge razor blade, make one ¼-inch-deep slash lengthwise down the center of each loaf. Carefully pour the boiling water into the empty baking pan on the bottom rack to create steam, then immediately place the loaf pans on the baking stone on the middle rack. Reduce oven temperature to 350°F (177°C). Bake until the crust is dark brown and the internal temperature registers 200°F (93°C), 40 to 50 minutes, rotating the pans 180° and side to side halfway through baking.
Cool and store: Transfer the pans to a wire rack and let cool in the pans for 5 minutes. Remove the loaves from the pans and return them to the wire rack to cool to room temperature, about 2 hours. Double-wrap the cooled loaves in plastic wrap and store at room temperature for up to 3 days, or wrap in an additional layer of aluminum foil and freeze for up to 1 month.