Raised Doughnuts

Yesterday I decided to try to make Raised Doughnuts for breakfast today, and knocked the ball out of the park! It turned out to be a project, but the results were well worth it.
This is going to be less than a doughnut recipe, because I used my Bread Machine Bread Dough Cinnamon Roll recipe I posted here back in April 2013 as the doughnut dough. This entry is more about process.
I am certain the cinnamon roll dough recipe can be adapted to handmade dough if you just look up some homemade yeast bread recipes online and adapt the ingredients to their method, so don't be upset or run away if you don't have a bread machine.
I will be including glaze recipes, though.
I mentioned that I first decided to make these yesterday. In fact, Aaron and I made the dough in the bread machine last night. We then put it in a bowl greased with cooking spray, and covered it with plastic wrap that was also coated with cooking spray on the underside, so if the dough should rise, it wouldn't stick to the bowl or plastic wrap. We placed the bowl into the refrigerator overnight.
This morning, I took the bowl out of the refrigerator, and prepared two cookie sheets by laying down parchment paper on them, and heated the oven just to warm it a bit (under 200 degrees F). I rolled the dough on floured parchment paper to about 1/3 of an inch thick, maybe 1cm, and cut it using a doughnut cutter, and placed the cut-out doughnuts and holes on the cookie sheets.  If you don't have a doughnut cutter, I would cut them into bars or sticks 1-2" thick. Once the sheet was full, I turned off the oven and placed it inside with the door of the oven cracked open to allow the doughnuts to rise for about 45 minutes.
I called Aaron over to help at this point. I had him put about 1/2-3/4 of an inch of oil into a large frying pan, and heated it over medium-low heat until a doughnut hole placed in the hot oil floated and fried to golden brown on the bottom in about 1-2 minutes. We then fried all of the doughnuts in the oil, flipping them once each, and let them cool on a cooking rack placed over more parchment paper in a large jellyroll pan to catch the drips.
This produced darn near perfect doughnut shop looking raised Doughnuts. Fluffy light. No joke.
We used a granulated sugar glaze because we were out of powdered sugar, and made the best sticky doughnuts you could imagine.
Here are three glaze or glazing/icing recipes I would use for these:

Granulated Sugar Glaze (Sticky Doughnuts)
Adapted from a recipe found at Our Everyday Life.

1 Cup granulated sugar
1 Cup water
A few drops vanilla extract

Combine water and sugar in a medium saucepan. Heat to a simmer over a medium-low heat while stirring, and simmer for about 5 minutes after the sugar dissolves and the mixture begins to thicken. Remove from heat and let cool for a few minutes, then add vanilla extract and mix it in. Allow to cool to room temperature, then glaze doughnuts by dropping them into the glaze and flipping them once before returning them to the cooling rack. These will crust like a traditional glazed doughnut, but it takes much more time-about an hour, compared to a couple of minutes for a powdered sugar glaze. If you want to eat these doughnuts warm, like any sane person, they will probably be sticky, and almost certainly delicious.

Powdered Sugar Glaze
Adapted from a recipe at epicurious.

1-1/2 Cups powdered (confectioners) sugar
2-3 Tbsp water or milk (water is used at most doughnut shops, and by me)
1/4 Tsp vanilla extract
A small pinch of salt

Put sugar into a mixing bowl and add water, salt and vanilla. Mix by hand until it is no longer seriously lumpy. Dip doughnuts into the glaze and coat them by flipping once, and return them to the cooling rack. The normal glaze crust should form in a minute or two.

Buttercream Icing
Adapted from a recipe at allrecipes.

1/2 Cup softened butter
2 Cups confectioners (powdered) sugar
3 Tbsp milk
1/2 Tsp vanilla
1/4 Tsp salt

Optional: 2-3 Tbsp cocoa powder for chocolate icing
1/2 Tsp Maple Extract or Mapline for Maple icing
1/2-1 Tsp Ground Cinnamon for a cinnamon frosting

Cream the softened butter by hand or using a mixer in a large mixing bowl until creamy. Gradually mix in the sugar until thoroughly incorporated (add in cocoa powder or ground Cinnamon to the sugar if using them). Mix in the salt and vanilla (and Maple Extract if making Maple icing). Pour in the milk and mix for 3 or 4 minutes. If the icing is too thick to slowly sheet off of the spoon, add more milk 1/2 Tsp at a time, mixing it in thoroughly until it does sheet off.. Drop doughnuts into the icing on one side, and return to the cooling rack icing side up. The crust should form in one to two minutes. If you want to spread this icing instead, use less milk and mix to a spreadable consistency.

All three of these glaze/icing recipes can be used on cakes, or Cinnamon rolls, or other pastries.