Preheat your oven to 350° F. Grease 2 donut pans with a nonstick cooking spray.
In a medium mixing bowl, whisk together the flour, the sugars, baking powder, salt, and cinnamon in a medium bowl.
With a spoon, (a wooden spoon works best) push the dry ingredients against the sides of the bowl to make a well. Add the eggs, oil, milk, and vanilla extract in the well and whisk to combine all.
In a small bowl, stir together the brown sugar and cinnamon to make the cinnamon swirl.
Spoon the doughtnut batter into a piping bag and pipe a small amount of batter into each donut cup.
Sprinkle the brown sugar/cinnamon mixture over the top of the each batter doughnuts.
Then top each donut off with the remaining batter to fill the cup. Place the doughnut filled pans in your preheated oven. Bake for 20 to 25 minutes, until the donuts bounce back when pressed lightly with your finger.
Remove from oven and allow to cool in the pan for 5 minutes, then transfer to a wire cooling rack to cool completely.
As the donuts are cooling, whisk together the powdered sugar, vanilla extract, and milk until smooth to make the king cake doughnut glaze.
After they are cool dip the top of each donut into the glaze and place it back on the wire rack.
Before the icing hardens decorate each king cake donut with the iconic purple, green, and gold sprinkles. Allow the glaze to harden before serving.