Preheat oven to 350°F.

In a large bowl whisk together the flour, sugar, baking powder, salt, and cinnamon; set aside.

In a small saucepan bring together the milk, white vinegar, vanilla, egg, and butter.

Cook over medium-heat, stirring constantly with a whisk until the butter melts, about one minute. Remove from heat.

Add the milk mixture into the flour mixture; mix until combined.

Using a large tablespoon, spoon the doughnut mixture into an ungreased doughnut pan.

Bake for 12 to 14 minutes, or until a toothpick inserted comes out clean.

Remove from oven and immediately invert the pan onto a cooling rack.

While the doughnuts are cooling, begin to work on the glaze. Place all the glaze ingredients in a small saucepan and cook over medium-heat, whisking constantly just until combined and no lumps appear.

Set the saucepan over a bowl filled with hot water.

Dip the doughnuts into the glaze, one at a time, and set on a rack, glaze side up. Put something underneath the rack because some of that glaze will drip off.

Give it a few minutes before you dig in.