Preheat your oven to 350°F (175°C) and grease your donut pan.
In a large mixing bowl, combine the gluten-free all-purpose flour, granulated sugar, baking powder, salt, and ground cinnamon. Whisk thoroughly.
In another bowl, beat the eggs and then add the milk, vegetable oil, and vanilla extract. Mix until well combined.
Pour the wet ingredients into the dry ingredients and gently stir until just combined.
Fill each cavity of the prepared donut pan about two-thirds full with the batter.
Bake for 10 to 12 minutes, or until lightly golden. Check for doneness with a toothpick.
Let the donuts cool for about 5 minutes, then transfer to a wire rack to cool completely. Prepare the glaze.
Dip the cooled donuts into the glaze and let them set on the wire rack.