In the bowl of a stand mixer fitted with the dough hook, dissolve the sugar in the lukewarm milk. Sprinkle the yeast over the milk and stir gently. Let it sit for 3 minutes until light and foamy.
Add flour, 3 tbsp butter, salt, pumpkin puree, and shredded cheddar cheese. Knead at medium speed until the dough is smooth and elastic.
Turn out the dough onto a lightly floured surface and knead for a few more minutes.
Place dough in a greased bowl, cover, and let rise in a warm place for about 1 hour until doubled.
Lightly grease two 12-count muffin pans with butter. Set aside.
Punch down the dough. Break off small pieces and roll into balls (about 1-inch diameter). Place three dough balls into each muffin cup.
Cover the muffin pan loosely with plastic wrap and let rise in a warm, draft-free area until doubled, about 20-30 mins. Make-Ahead Note: The assembled muffin pan can be wrapped in plastic wrap and refrigerated overnight. Let the dough come to room temperature for 30 minutes before baking.
Meanwhile, preheat your oven to 375°F (190°C).
Brush the tops of the dinner rolls with butter and bake for 16-20 minutes until the tops are golden. Take the rolls out and brush with more butter, if desired.
Serve warm! Leftover Pumpkin Dinner Rolls also freeze great. Take them out of the freezer a few hours before you want to serve them and reheat in the oven at 300°F, about 5-10 minutes.