Dissolve yeast and sugar in warm water in a large bowl, and let stand for 5 minutes. Stir in milk and eggs. Lightly spoon the flour into dry measuring cups, and level with a knife. Add 3 cups flour, margarine, and salt to yeast mixture, and stir until blended. Turn the dough out onto a lightly floured surface. Knead until smooth and elastic (about 10 minutes); add enough of remaining flour, 1 tablespoon at a time, to prevent dough from sticking to hands.
Place dough in a large bowl coated with cooking spray, turning to coat top. Cover dough, and let rise in a warm place (85°), free from drafts, 1 hour or until doubled in bulk. Punch dough down; cover and let rest for 5 minutes. Divide dough into 16 equal portions. Working with 1 portion of dough at a time (cover remaining dough to keep from drying), remove 1 rounded teaspoon of dough from each portion, and set aside. Place the larger portions of dough in muffin cups coated with cooking spray. Make a deep indentation in the center of each portion using a floured finger. Shape the reserved pieces of dough into balls. Press one dough ball into each indentation. Cover and let rise 30 minutes or until doubled in bulk.
Preheat oven to 375°.
Uncover dough. Combine 1 tablespoon water and egg white; brush over dough. Bake at 375° for 25 minutes or until golden brown. Serve warm.