For the Biga: Combine 2 cups bread flour, 1 cup water, and 1/2 teaspoon yeast in large bowl and stir with wooden spoon until uniform mass forms and no dry flour remains, about 1 minute. Cover bowl tightly with plastic wrap and let stand at room temperature (70 degrees) overnight (at least 8 hours and up to 24 hours).
For the Soaker: Combine 3 cups whole-wheat flour, 1/2 cup wheat germ, and 2 cup milk in large bowl and stir with wooden spoon until shaggy mass forms, about 1 minute. Turn out dough onto lightly floured work surface and knead until smooth, 2 to 3 minutes. Return soaker to bowl, cover tightly with plastic wrap, and refrigerate overnight (at least 8 hours and up to 24 hours).
For the Dough: Tear soaker apart into 1-inch pieces and place in bowl of stand mixer fitted with dough hook. Add biga, honey, salt, yeast, butter, and oil. Mix on low speed until cohesive mass starts to form, about 2 minutes. Increase speed to medium and knead until dough is smooth and elastic, 8 to 10 minutes. Turn out dough onto lightly floured counter and knead 1 minute. Shape dough into ball and place in lightly greased container. Cover tightly with plastic wrap and allow to rise at room temperature 45 minutes.
Gently press down on center of dough to deflate. Holding edge of dough with fingertips, fold partially risen dough over itself by gently lifting and folding edge of dough toward middle. Turn bowl 90 degrees; fold again. Turn bowl and fold dough 6 more times (total of 8 folds). Cover and allow to rise at room -temperature until doubled in volume, about 45 minutes.
Adjust oven racks to middle and lowest positions, place baking stone on middle rack, and heat oven to 400 degrees. Spray two 81/2 by 41/2-inch loaf pans with nonstick cooking spray. Transfer dough to well-floured counter and divide into 2 pieces. Working with 1 ball of dough at a time, pat each into 8 by 17-inch rectangle. With short side facing you, roll dough toward you into firm cylinder, keeping roll taut by tucking it under itself as you go. Turn loaf seam side up and pinch it closed. Place loaf seam side down in prepared loaf pan, pressing gently into corners. Repeat with second ball of dough. Cover loaves loosely with plastic wrap and allow to rise at room temperature until almost doubled in size, 60 to 90 minutes (top of loaves should rise about 1 inch over lip of pan).
Place empty loaf pan or other heatproof pan on bottom oven rack and bring 2 cups water to boil on stovetop. Using sharp serrated knife or single-edge razor blade, make one ¼-inch-deep slash lengthwise down center of each loaf. Pour boiling water into empty loaf pan in oven and set loaves on baking stone. Reduce oven temperature to 350 degrees. Bake until crust is dark brown and internal temperature registers 200 degrees on instant-read thermometer, 40 to 50 minutes, rotating loaves 180 degrees and side to side halfway through baking.
Transfer pans to wire rack and let cool 5 minutes. Remove loaves from pans, return to rack, and cool to room temperature, about 2 hours.