In a large mixer bowl combine 1 cup of the all-purpose flour and the yeast. Stir together warm water, the honey, oil, and salt; add to mixer bowl along with egg and egg yolk. Beat with electric mixer on low speed for 30 seconds, scraping sides with spatula.
Beat on high speed for 3 minutes. Using a spoon, stir in all of the whole wheat flour and as much of the remaining all-purpose flour as you can.
On a lightly floured surface knead in enough of the remaining all-purpose flour to make a moderately stiff dough (6 to 8 minutes). Place in a greased bowl; turn once to grease surface of dough. Cover; let dough rise in a warm place until double (1 to 1 1/4 hours).
Punch dough down. Cover; let rest 10 minutes. Remove and reserve about 1 cup dough; cover and set aside. Divide remaining dough in half. On a lightly floured surface roll each half into a 30-inch-long rope. On a greased baking sheet, shape one rope into a triangle, joining ends about one-third of the way down on one side. Join one end of the second rope to the triangle about one-third of the way down, on the opposite side from where you joined the ends of the first rope. Form a star by weaving the second rope alternately over and under the first dough triangle. Press ends of dough tightly to seal.
Divide reserved dough into 6 pieces. Roll each into an 8-inch-long rope, about 1/4 inch in diameter. Cut each rope in half and, with the 2 halves, form an X over each place where the triangles overlap. Tuck ends of short ropes under the bread to secure.
To help the bread retain its star shape, make six 1-inch triangular pieces of foil. Push foil into the holes that form the star points.
Cover and let rise in a warm place until nearly double (30 to 60 minutes). Mix together the remaining egg white and 1 tablespoon water; brush over loaf. Sprinkle with sesame or poppy seed.
Bake in a 350 degrees F oven for 25 to 30 minutes or until golden. Cover with foil during the last 10 minutes to prevent overbrowning, if necessary. Cool on rack. Makes 1 loaf (16 servings).