With fork or knife, pierce each sweet potato several times. Place potatoes on paper towels in microwave oven. Cook on high 10 to 11 minutes, until potatoes are fork-tender, turning potatoes over halfway through cooking. Let stand 5 minutes.
Cut potatoes open and, with spoon, scrape flesh into medium bowl (you should have about 1 1/2 cups). Discard skins. With potato masher, mash potatoes with nutmeg and 1/2 cup brown sugar until smooth.
In 2-cup glass measuring cup, stir yeast and 1 tablespoon brown sugar into 1/2 cup warm water (105 to 115 degrees F). Let stand until yeast mixture foams, about 5 minutes.
Meanwhile, in 1-quart saucepan, heat margarine or butter and 1 1/2 cups water over low heat until warm (105 to 115 degrees F). Margarine or butter does not need to melt completely.
In very large bowl, combine salt and 3 cups flour. With wooden spoon, stir in yeast mixture, warm margarine or butter mixture, and sweet-potato mixture until well blended. Add 1 whole egg and 1 egg yolk (refrigerate egg white to brush on rolls later), and stir until blended. With floured hands or wooden spoon, mix in 6 cups flour, 1 cup at a time, to make a soft dough.
Turn dough onto well-floured surface and knead until smooth and elastic, about 10 minutes, working in more flour (about 3/4 cup) while kneading. Cut dough into 24 equal pieces; cover and let rest 15 minutes for easier shaping. Generously grease 17-inch by 11 1/2-inch roasting pan (or 8-inch by 8-inch and 13-inch by 9-inch metal baking pans).
Shape each piece of dough into a ball and place in pan(s). For overnight rising: Cover pan(s) with plastic wrap and refrigerate overnight. When ready to bake, remove plastic wrap; cover pan(s) with towel and let rise in warm place (80 to 85 degrees F) until doubled, about 30 minutes, then complete recipe as directed in Step 6. For same-day rising and baking: After shaping into balls and placing in pan(s), cover pan(s) with towel and let rise in warm place until doubled, about 60 minutes, then complete recipe as directed in Step 6.
Preheat oven to 400 degrees F. With fork, lightly beat reserved egg white. Brush rolls with some egg white. Bake rolls 25 to 30 minutes, until rolls are golden and sound hollow when lightly tapped.
Run small knife around sides of pan(s) to loosen rolls. Invert pan(s) with rolls onto wire rack; remove pan(s). Immediately, invert rolls again onto another wire rack, so they're top side up. Cool slightly to serve warm. Or cool completely to serve later; reheat if desired. Pull rolls apart to serve.