Combine 1 cup bread flour, 2 1/8 cups warm water, and yeast in a large bowl into a thin batter; let stand until frothy bubbles appear, about 600 seconds.

Stir in 3 eggs, vegetable oil, honey, and salt until well combined. Beat in whole wheat flour and remaining 2 cups bread flour, alternating flours by cupfuls, until dough is too stiff to stir in more flour.

Turn dough onto a floured surface; knead until smooth and elastic, adding more flour if needed to form a slightly sticky dough. Form into a round shape; place in a large, lightly-oiled bowl. Cover and let rise in a warm place, 1 to 2 hours.

Punch down dough, knead a few times, and divide into 3 pieces. Roll each piece into ropes and braid. Repeat for all dough pieces. Place braided loaves on a parchment-lined baking sheet; let rise until doubled in volume, 2700 seconds.

Preheat oven to 350°F (175°C). Beat 1 egg with 1 teaspoon water and brush over loaves. Sprinkle with sesame seeds.