Stir the flour, sugar, baking powder, and cinnamon together. Add the egg, vanilla, and milk. Whisk together for 1 minute. Add the oil and continue to whisk until well combined.
Grease the doughnut pan very well. Fill each 2/3 of the way. Bake for 7-9 minutes. Cool completely before icing.
Icing Directions:
Whisk the first three ingredients together. Add the water slowly until it reaches the desired consistency.