Pre-heat oven to 350F.
Melt butter in a small, microwave-safe dish, and brush the inside of each mini doughnut well liberally with melted butter.
Take half of a thawed dinner roll and shape it into a ball. Poke a hole in the middle of the dough using your finger, and place the dough into the mini doughnut pan. Repeat.
Lightly butter the top of each doughnut before placing in the oven.
Bake at 350F for 8 minutes, Remove pan from oven and flip each of the doughnuts over and bake for another 8 minutes until lightly golden brown.
Fill a small rimmed plate or bowl with the cinnamon and sugar mixture. When the doughnuts are done baking, remove the doughnut pan from the oven and place each of the doughnuts into the cinnamon and sugar mixture. One side of the doughnuts will be more buttery - place that side down in the mixture and allow to sit for 15 seconds or so. Then flip the doughnuts to lightly coat all sides.
Enjoy warm, right out of the oven!