Place warm water in a large warm mixer bowl. Sprinkle in yeast; stir until dissolved. Add warm milk, sugar, butter, salt, eggs and 2 cups flour; beat 2 minutes at medium speed of electric mixer. Stir in enough remaining flour to make soft dough. Knead on lightly floured surface until smooth and elastic, about 4 to 6 minutes. Place in greased bowl, turning to grease top. Cover; let rise in warm, draft-free place until doubled in size, about 30 to 45 minutes.
Remove dough to lightly floured surface; divide into 12 equal pieces*. Form each piece into smooth ball. Place on large greased baking sheet. Flatten balls to 4-inch rounds; cover. Let rise in warm, draft-free place until doubled in size, about 20 to 40 minutes. Just before baking, gently brush buns with beaten egg, then sprinkle with minced onion, poppy seeds or sesame seeds, if desired.
Bake in preheated 400°F oven for 10 to 15 minutes or until done. Remove from baking sheet; let cool on wire rack.
*Sliders Variation: To make slider size buns instead of full size burger buns, divide and shape dough into 24 equal balls and flatten to 2-1/2-inch rounds. Bake as directed for 8 to 10 minutes.