Lightly spoon flour into dry measuring cups; level with a knife. Combine 2 cups flour, warm milk, and yeast in a large bowl. Cover with plastic wrap, and let stand 1 1/2 hours (batter should become very bubbly and almost triple in size).
Add 3 cups flour, sugar, butter, salt, and egg; stir with a wooden spoon 3 minutes or until well combined. Turn dough out onto a lightly floured surface. Knead until smooth and elastic (about 8 minutes); add enough of remaining 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 1/2 hours or until doubled in size. (Lightly press two fingers into dough. If indentation remains, the dough has risen enough.)
Turn dough out onto a lightly floured surface; lightly dust dough with flour and pat into an 10 x 8-inch rectangle. Divide dough by making 3 lengthwise cuts and 4 crosswise cuts to form 20 equal pieces; shape each piece into a ball. Place balls in a 13 x 9-inch baking pan coated with cooking spray.
Lightly coat the dough with cooking spray. Cover with plastic wrap, and let rise in a warm place (85°), free from drafts, 1 hour or until doubled in size.
Preheat oven to 375°.
Brush 3 tablespoons milk lightly over dough; sprinkle with poppy seeds. Bake at 375° for 20 minutes or until browned. Cool rolls in pan 5 minutes. Serve warm, or cool completely on a wire rack.
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