In a large bowl, dissolve the yeast and sugar in the warm water. Let sit for 10 minutes., While yeast is getting started, melt butter and let it cool., Add cooled butter, salt, cinnamon, eggs, flour, and mashed vegetable to yeast mixture, stirring to blend; dough will be quite slack., Beat with the flat beater of an electric mixer, or stir by hand, for about 5 minutes., Place dough in a well-greased bowl, turning to coat all sides, and cover with plastic wrap; or scoop into a large, well-oiled plastic bag, sealing bag near the top. Refrigerate dough 8 hours, or overnight., Next day, remove dough from refrigerator, and place on a lightly floured surface., Divide dough into 24 pieces, rolling each piece into a ball; being cold, the dough will be quite easy to work with. If it it's overly sticky, rub your hands with a bit of oil., Place rolls in a lightly greased large, round pan — a 14" deep-dish pizza pan works well — or two lightly greased 9" or 10" cake pans. Set aside to rise for about 3 hours, or until rolls fill the pan., Bake rolls in a preheated 375°F oven for about 20 minutes, or until they're lightly browned.