In a small bowl, sprinkle yeast and 1 tablespoon sugar in the 1/2 cup lukewarm water and stir to dissolove. Let stand until foamy, about 5 to 10 minutes. In a large bowl, mix butter, remaining sugar, salt, potato flakes, and hot water together until combined. Let cool to lukewarm. Add yeast mixture and 1 cup of flour to the potato mixture. Beat with an electric mixer at medium speed until smooth, about 2 minutes. Scrape bowl occasionally. Gradually add the rest of the flour, one cup at a time, beating to make a soft dough. Place dough in a large greased bowl -- turn to grease the top. Cover with plastic wrap and let rise in a draft-free warm place until doubled, about 1-1/2 hours.

Turn dough out onto lightly floured surface and knead 6 or 8 turns to remove air. Let rise about 10 minutes. Lightly grease or line a large baking pan (or 2 smaller pans) with parchment paper. Divide dough into 24 equal pieces. Cup your hand over 1 piece, and using your thumb and pinkie to keep ball inside your cupped hand, push dough with heel of your hand against work surface while rolling in a circular motion to form a smooth ball. Repeat with remaining dough pieces, setting balls about 1-inch apart on prepared baking pan(s). Brush tops carefully with melted butter. Loosely cover with plastic wrap and let rise in a draft-free warm place until doubled in bulk, about 45 to 60 minutes (rolls should be touching at this point).

Put oven rack in middle position and preheat oven to 375 degrees F. Bake rolls until golden brown, about 15 to 20 minutes. Watch carefully -- do not overbake. As soon as rolls come out of oven, brush tops again with melted butter.