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.

Add remaining 1 3/4 cups water to the bowl of an electric mixer fitted with the dough hook attachment, along with remaining 3 tablespoons honey, butter, caraway seeds, and salt. Mix on low to combine. Gradually add both flours, one cup at a time, 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 caraway 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 on a conventional oven or 425 degrees on a convection oven. Reduce oven temperature to 400 degrees (conventional) or 375 degrees (convection).