Prepare the bread according to your choice of techniques below.
Bread Machine Instructions:
Add all the ingredients, except the Cinnamon Topping in the bread pan of bread machine. Process according to manufacturer's instructions for a dough setting. Do not be afraid to open the lid and check the dough. It should form a nice elastic ball. If you think the dough is too moist, add additional flour (a tablespoon at a time). The same is true if the dough is looking dry and gnarly. Add warm water (a tablespoon at a time).
If you can not judge your dough by looking, stick your finger in and feel the dough. It should be slightly tacky to the touch. When the bread machine has completed the dough cycle, remove the dough from the pan to a lightly floured surface. Knead the dough several times and form the dough into an oval; cover with plastic wrap and let rest for 10 to 15 minutes.
Stand Up Mixer Instructions:
In a large bowl or in the bowl of a 5-quart stand mixer, combine all the ingredients in the order given except the Cinnamon Topping. Using a dough hook, mix all the ingredients together into a uniform dough. It should form a nice elastic ball. If you think the dough is too moist, add additional flour (a tablespoon at a time). The same is true if the dough is looking dry and gnarly. Add warm water (a tablespoon at a time).
Turn the dough out onto a floured surface and knead until elastic, about 10 minutes. Cover the bowl with plastic wrap and let rest for 10 to 15 minutes.
Roll dough out approximately 1/3- to 1/2- inch thick on a lightly-floured board. Using your floured doughnut cutter, cut out the doughnuts and place on a parchment-lined baking sheet (I like to use my silicone baking mats). If you don't have a doughnut cutter, use a 2 to 3-inch round cookie cutter. Cut out the smaller inner circle using a smaller cutter. Cover the doughnuts with plastic wrap and let rise for approximate 45 to 60 minutes.
At this point, the unbaked doughnuts can be covered with plastic wrap and refrigerated overnight (I have actually made them two days in advance). They can be either baked upon removing from the refrigerator or let come to a room temperature (I have done both ways). They do a slow rise overnight and it is not necessary to let them come to room temperature before baking.
Preheat oven to 375 degrees F. Bake for approximately 8 minutes or until the bottoms of the doughnuts are just golden. Do not overbake - under bake them a little, as they will continue baking outside the oven for a few minutes. You want an interior that is moist and tender. Remove from oven and let the doughnuts cool for 1 to 2 minutes.
Dip each doughnut in the melted butter and then in the sugar/cinnamon mixture.
Makes approximately 1 1/2 to 2 dozen doughnuts.
While the doughnuts are baking, place the melted butter in a bowl and place and sugar and cinnamon in a separate bowl.
Baked Sugar Doughnuts Recipe: https://whatscookingamerica.net/bread/bakeddoughnuts.htm