Soften yeast in water. Combine in mixing bowl milk, butter, sugar, and salt. Cool to lukewarm. Blend in egg and yeast. Gradually add flour to form a stiff dough; beat well after each addition. Cover. Let rise in a warm place until light, about 1 hour.
Combine cheese and onion. Roll out dough, 1/2 at a time, on floured surface to 14x8 rectangle. Cut into 7x2 inch pieces. Place about 3 rounded tablespoons cheese down center of each. Bring edges to center; seal. Seal ends. Place seam-side down, on cookie sheets. Repeat with remaining dough. Let rise in warm place, 30 minutes.
Fry in heavily-buttered skillet on medium heat, about 2 minutes on each side. Turn carefully to brown all sides. Add butter as needed. Serve hot.