In a small bowl or liquid measuring cup, sprinkle yeast over 1/2 cup water. Add 2 teaspoons honey. Whisk until yeast dissolves. Let stand until foamy, about 5 minutes.

Transfer to the bowl of a mixer fitted with the dough hook. Add butter and remaining 1 3/4 cups plus 2 tablespoons water and 3 tablespoons honey. Whisk together all-purpose, whole-wheat, and rye flours with salt; add 3 cups to yeast mixture. Mix on low speed until smooth. Add remaining 3 1/4 cups flour mixture, 1 cup at a time. Add wheat berries, bulgur, 1/2 cup oats, 1/2 cup flaxseed, and 1/3 cup sunflower seeds; mix on low to combine. Continue mixing until dough comes away from sides of bowl and forms a ragged, slightly sticky ball.

Butter a large bowl. Knead dough on a floured surface until smooth and elastic but still slightly tacky, about 5 minutes. Shape into a ball. Transfer to prepared bowl; cover with plastic wrap.

Let dough stand in a warm place until it doubled in volume (it should not spring back when pressed), about 1 hour. Butter two 4 1/2-by-8 1/2-inch loaf pans. Punch down dough and divide in half.

Working with one piece of dough at a time, shape into a 7-by-7-inch square. Fold dough into thirds; press seam to adhere and pinch ends to seal. Place seam side down in loaf pan. Repeat process with remaining piece of dough.

In a small bowl, mix egg white with 1 teaspoon water and brush mixture over tops of loaves; sprinkle with remaining 2 tablespoons rolled oats, remaining 1 tablespoon flaxseeds, and remaining 2 tablespoons sunflower seeds.

Spray two pieces of plastic wrap with nonstick cooking spray; drape loaves with prepared plastic wrap and let stand until dough rises about 1 inch above tops of pans, 45 minutes to 1 hour.

Preheat oven to 450 degrees for conventional, 425 degrees for convection. Reduce oven temperature to 400 degrees (conventional) or 375 degrees (convection).