Stir the 2 teaspoons honey into warm water in small bowl until well blended. Sprinkle yeast over top. Let stand until mixture is foamy, 5 to 10 minutes.
Meanwhile, whisk together the remaining 1/4 cup honey, the milk, egg and salt in small saucepan until well blended. Add the butter. Heat over low heat, stirring until the butter is melted. Remove saucepan from heat and let cool until mixture registers 115 degrees F to 120 degrees F on an instant-read thermometer. Pour into a large bowl.
Beat 1 cup whole-wheat flour and 1 cup bread flour into the butter mixture in the bowl with a wooden spoon until the mixture is smooth. Add yeast mixture, wheat-and-barley cereal, oats and sunflower seeds; stir to combine.
Stir in remaining flours, 1/2 cup at a time, until dough pulls away from the sides of bowl.
Transfer to lightly floured surface. Knead until smooth and elastic, 8 to 10 minutes, adding more flour as needed to prevent sticking. Place in well-greased bowl, turning to coat. Cover with clean kitchen towel or plastic wrap. Let rise in warm place until doubled in volume, about 1 hour.
Punch dough down. Let rest for 5 minutes. Shape into 6-inch round loaf. Transfer to greased baking sheet. Cover with kitchen towel. Let rise until doubled in volume, 30 to 45 minutes.
Twenty minutes before bread has completed the second rise, heat oven to 375 degrees F.
Mix sunflower seeds and oats in bowl. Brush top of risen loaf with egg white. Sprinkle top evenly with seed mixture.
Bake in 375 degree F oven for 30 to 35 minutes or until loaf sounds hollow when lightly tapped on bottom. Remove to wire rack to cool. Makes 1 round loaf (12 slices).