Preheat oven to 375°F and lightly spray a mini donut pan, wiping off the overspray with a paper towel.
In a bowl, whisk together the flour, sugar, baking powder, salt, and baking soda until blended.
In another bowl, whisk together the egg, milk, sour cream, vegetable oil, and vanilla.
Pour the wet ingredients into the dry ingredients and stir until just combined, being careful not to overmix.
Pipe or spoon the batter into the donut pan cavities, filling each about ¾ full.
Bake for about 8 to 10 minutes, or until the donuts spring back when touched. Remove from oven and let sit in pan for 3 to 4 minutes, then transfer to a wire rack to cool completely.
Meanwhile, whisk together the glaze ingredients until smooth and pourable. Adjust milk to reach the right consistency.
When the donuts are fully cooled, dip each one into the glaze, allow excess to drip off, and place back on the wire rack until the glaze sets.
Serve fresh, or store in an airtight container at room temperature for up to 2 to 3 days.