In a large mixing bowl, sprinkle the yeast onto the very warm water. Add sugar and "proof" the yeast (is it clumping? then is proofed that it is working) Stir in the applesauce and egg and add the flour until the dough is easy to handle (between 6 1/2 to 7 cups). Cover with wax paper and then cover that with a damp (not wet) tea towel. Place in refrigerator. Keep the towel damp and you will have rolls for up to 5 days (if there is any still there in 5 days).
About an hour or 2 before baking, spray muffin tins with non-stick spray. Shape rolls - if using regulare muffin tins, 3 walnut size balls makes cloverleaf rolls or one large ball can be cut with a scissors (top) at right angles for 4ths of left as one large ball as a roll. OR use mini-muffin pans - one walnut size ball per roll. Either way, bake at 400 for about 15 minutes (until golden brown). Gently butter tops and remove from pans into a bread basket and serve.