Dissolve yeast in 2 cups warm water in a large bowl; let stand 5 minutes. Add honey, oil, and 1/2 teaspoon salt, stirring with a whisk. Lightly spoon flour into dry measuring cups; level with a knife. Add 3 cups flour and bran to yeast mixture, stirring until combined. Cover and let stand in a warm place (85°), free from drafts, 1 hour or until small bubbles appear on surface.
Add remaining 1 teaspoon salt, 2 cups flour, 1/4 cup sunflower seeds, 1/4 cup sesame seeds, 1 1/2 teaspoons black pepper, and 1 1/2 teaspoons green pepper; stir until dough forms. Turn dough out onto a floured surface. Knead until smooth and elastic (about 8 minutes); add enough of remaining flour, 1 tablespoon at a time, to prevent dough from sticking to hands (dough will feel tacky). Place dough in a large bowl coated with cooking spray, turning to coat top. Cover and let rise in a warm place (85°), free from drafts, 45 minutes or until doubled in size. (Gently press two fingers into dough. If indentation remains, dough has risen enough.) Punch dough down; cover and let rest 5 minutes.
Divide dough in half; place each half in an 8 x 4-inch loaf pan coated with cooking spray. Cover and let rise in a warm place (85°), free from drafts, 45 minutes or until doubled in size.
Preheat oven to 400°.
Brush loaf tops with egg; sprinkle tops evenly with remaining 1 tablespoon sunflower seeds, remaining 1 tablespoon sesame seeds, remaining 3/4 teaspoon black pepper, and remaining 3/4 teaspoon green pepper. Bake at 400° for 35 minutes or until loaves are browned on bottom and sound hollow when tapped. Remove loaves from pans, and cool on wire racks. Cut each loaf into 8 slices.