Stir together yeast, 1/4 c warm water, and 1 t. sugar in a 2 cup glass measuring cup; let stand 5 minutes.
Beat 2 T. sugar, softened butter, and salt at medium speed with a heavy-duty electric stand mixer until creamy. Add egg, milk, and yeast mixture, beating until blended. Gradually add flour, beating at low speed until smooth. Turn dough onto a well floured surface, and knead until smooth and elastic (2-3 minutes). Place in a well-greased bowl, turning to grease top.
Cover and let rise in a warm place(85), free from drafts, 30 minutes or until doubled in bulk.
Preheat oven to 400. Punch dough down; turn dough out onto a floured surface. Divide dough into 24 pieces; shape into balls. Place in 2 greased 9: square pans. Cover and let rise in a warm place (85), free from drafts, 15 minutes.
Bake at 400 for 15 minutes or until golden. Brush tops with melted butter, and serve immediately.