Stir whole-wheat flour, bran, and 1 cup water in a bowl. Let stand 30 minutes.
Stir milk and 1 tablespoon sugar in a bowl until sugar dissolves. Stir in yeast. Let stand until foamy, about 5 minutes.
Put whole-wheat flour mixture, milk mixture, remaining 3 tablespoons sugar, the cornmeal, 3 tablespoons oats, the ground flaxseed, and salt into the bowl of an electric mixer fitted with the dough hook; mix on medium-low speed until combined. Add 2 1/2 cups bread flour; mix until dough is tacky, but not sticky, about 2 minutes (if dough is too sticky, add more flour, 1 teaspoon at a time). Continue kneading until dough is soft and elastic, about 5 minutes more.
Coat a large bowl with cooking spray. Add dough to bowl; turn to coat. Cover loosely with plastic wrap. Let dough rise in a warm, draft-free place until doubled in bulk, about 1 hour (or refrigerate overnight; bring to room temperature).
Turn out dough onto a work surface; shape into a loaf about 9 inches long. Using a spray bottle, mist with water; sprinkle top with remaining 2 teaspoons oats and the whole flaxseed. Coat a 9-by-5-inch loaf pan and a piece of plastic wrap with cooking spray. Transfer loaf to the pan, and cover lightly with the plastic wrap. Let stand until doubled in bulk, about 45 minutes.
Preheat oven to 400 degrees. Mist oven with water; place loaf in oven. Bake 5 minutes; mist oven again. Continue to bake, rotating pan once, until well browned, 25 to 30 minutes. Unmold bread onto a wire rack; return to oven, and bake directly on oven rack 5 minutes more. Remove from oven; let cool completely on rack. Bread can be stored, wrapped in plastic, at room temperature up to 1 week.
This bread also can be made in a two-pound-capacity bread machine: Add all the ingredients (using 2 3/4 cups bread flour), and bake according to the manufacturer's instructions. The resulting loaf will have a softer, paler crust than one baked in an oven. Cornmeal isn't always whole-grain, so check the label; avoid packages that say "degerminated."