The Bread is in the Baking

This is really tasty, but not like any doughnut you've every had. It's very bread-like, but sweet and a little flaky. If you think this recipe is going to be healthy because it's baked, it's not: you dip these doughnuts in butter. I got this recipe off of this site, which has a lot of other great recipes you should check out too.
I've changed the recipe a tiny bit, but not a lot. Mostly, I've made some of the ingredients less specific.

Baked Doughnuts
1 1/3 cups warm milk
1 packet active dry yeast (2 1/4 teaspoons)
2 tablespoons butter
2/3 cup sugar
2 eggs
5 cups all-purpose flour
A pinch or two of nutmeg, freshly grated (optional, I haven't used it)
1 teaspoon salt

Toppings
1/2 cup unsalted butter, melted
1 1/2 cups sugar
1 tablespoon cinnamon

Place 1/3 cup of the warm milk in the bowl of an electric mixer. Stir in the yeast and set aside for five minutes or so. Be sure your milk isn't too hot or it will kill the yeast. Stir the butter and sugar into the remaining cup of warm milk and add it to the yeast mixture. With a fork, stir in the eggs, flour, nutmeg, and salt - just until the flour is incorporated. With the dough hook attachment of your mixer beat the dough for a few minutes at medium speed. If your dough is overly sticky, add flour a few tablespoons at a time. Too dry? Add more milk a bit at a time. You want the dough to pull away from the sides of the mixing bowl and eventually become supple and smooth. Turn it out onto a floured counter-top, knead a few times (the dough should be barely sticky), and shape into a ball.

You can also do all of the above by hand.

Transfer the dough to a buttered (or oiled) bowl, cover, put in a warm place (a slightly heated oven works too) and let rise for an hour or until the dough has roughly doubled in size.

Punch down the dough and roll it out 1/2-inch thick on your floured countertop. You can cut out your doughnuts with a big round cookie cutter or a large mug, just press down firmly on the rolled out dough. you can use a smaller cookie cutter or a shot glass to stamp out circles.

NOTE: You may have trouble getting your dougnuts moved after stamping out the center so try to do it on the baking sheet your going to use.

Transfer the circles to a parchment-lined baking sheet. Cover with a clean cloth and let rise for another 45 minutes. Preheat your oven to 375 degrees as you wait for your dough to rise again.

Bake until the bottoms are just golden, 8 to 10 minutes. Start checking at 8 minutes. While the doughnuts are baking, place the melted butter in a medium bowl. Place the sugar and cinnamon in a separate bowl.

Remove the doughnuts from the oven and let cool for just a minute or two. Dip each one in the melted butter and a quick toss in the sugar bowl. Eat immediately if not sooner. They taste best warm!

Makes 1 1/2 - 2 dozen medium doughnuts.