In large bowl, mix bread flour, honey, salt and yeast. Add warm water, butter and egg. Beat with electric mixer on low speed 1 minute, scraping bowl frequently. Beat on medium speed 1 minute, scraping bowl frequently. Stir in enough whole wheat flour to make dough easy to handle.
On lightly floured surface, knead dough about 5 minutes or until dough is smooth and springy. Grease large bowl with shortening or spray with cooking spray. Place dough in bowl, turning dough to grease all sides. Cover bowl loosely with plastic wrap; let rise in warm place about 1 hour or until it doubles in size. Dough is ready if indentation remains when touched.
Grease bottom and sides of 13x9-inch pan with shortening or spray with cooking spray. In small bowl, mix egg white and 1 teaspoon water with fork. Gently push fist into dough to deflate. Divide dough into 15 equal pieces. Shape each piece into a ball. Brush top of each ball with egg white mixture. Dip tops of 8 balls into sesame seed and tops of 7 balls into poppy seed. Arrange seed side up in checkerboard pattern in pan. Cover pan loosely with plastic wrap; let rise in warm place 45 to 60 minutes or until the balls double in size.
Heat oven to 375°F. Bake 17 to 21 minutes or until golden brown. Remove from pan to cooling rack. Serve warm or cooled.