Dissolve yeast in warm water in a large mixing bowl; let stand for 5 minutes. Add 1 cup milk, butter, sugar, and 1 egg, and beat with a mixer at medium speed until well blended. Lightly spoon flours into dry measuring cups; level with a knife. Add 3 cups all-purpose flour and whole wheat flour to yeast mixture, and beat until blended. Let stand 15 minutes. Add salt, and beat well. Stir in 2 cups all-purpose flour to make a soft dough.
Turn the dough out onto a floured surface; knead until smooth and elastic (about 10 minutes). Add enough of remaining flour, 1/4 cup at a time, to keep dough from sticking to hands (dough will feel tacky). Place the 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 the dough. If indentation remains, the dough has risen enough.)
Heat oil in a large nonstick skillet over medium-high heat. Add onion; cook 10 minutes or until golden.
Preheat oven to 375°.
Punch dough down; cover and let rest 5 minutes. Divide in half. Working with 1 portion at a time, roll each portion into a 14-inch circle. Spread half of onion mixture over each portion, and cut each portion into 12 wedges. Roll up each wedge tightly, beginning at the wide end. Place, point sides down, on baking sheets coated with cooking spray. Combine 1 egg and 1 tablespoon milk, stirring with a whisk; brush over rolls. Sprinkle evenly with poppy seeds. Let rise, uncovered, 30 minutes or until doubled in size.
Bake at 375° for 23 minutes or until golden.