Place 1/3 cup flaxseed in a blender or clean coffee grinder, and process until ground to measure 1/2 cup flaxseed meal; set aside.
Dissolve sugar and yeast in warm water and warm milk in a large bowl; let stand 5 minutes. Lightly spoon flours into dry measuring cups; level with a knife. Add flaxseed meal, whole-wheat flour, 1 1/2 cups all-purpose flour, salt, and oil to yeast mixture; stir to form a soft dough. Turn dough out onto a floured surface. Knead until smooth and elastic (about 10 minutes); add enough of remaining all-purpose 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, 1 hour or until doubled in size. (Press two fingers into dough. If the indentation remains, the dough has risen enough.) Punch dough down; cover and let rest 5 minutes.
Divide dough into 18 equal portions, shaping each portion into a ball (cover remaining dough while working to prevent it from drying). Place balls 2 inches apart on a large baking sheet coated with cooking spray. Cover and let rise 45 minutes or until dough is doubled in size.
Preheat oven to 425°.
Uncover rolls; cut a 1/4-inch-deep "X" in top of each roll. Combine 1 tablespoon water and egg white, and brush over rolls. Sprinkle rolls with 2 tablespoons flaxseed. Bake at 425° for 15 minutes or until rolls are browned on the bottom and sound hollow when tapped. Remove rolls from pan.
Note: These rolls freeze well. To freeze, cool rolls completely and store in a zip-top freezer bag. When ready to use, remove rolls from bag and thaw completely. Preheat oven to 350º. Place rolls on a baking sheet; cover with foil, and bake until heated, about 8 minutes.