Preheat the oven to 350 degrees F. Spray or grease two donut pans.

Add the cake mix, eggs, oil, milk, and vanilla extract to a large mixing bowl and mix with an electric mixer on medium, until well combined.

Fill each donut cavity about 1/2 of the way full with the batter. Either spoon the batter in or transfer the batter to a ziplock bag or piping bag and pipe it into the donut pan cavities. (If there is any leftover batter after filling the donut pans, cover it and place in the refrigerator. Once the first round of donuts are baked and removed from the pans, add the remaining batter to the pans and bake.)

Bake in a preheated oven for 9-10 minutes. A toothpick inserted into a donut should come out with a few moist crumbs on it or clean.

Set the baked donut pans onto a cooling rack for about 10 minutes, then remove the donuts from the pan and set onto cooling racks to cool completely.

While the donuts are cooling, prepare the glaze.

In a mixing bowl, add the melted butter, confectioners sugar, corn syrup and about three tablespoons of milk.

Mix well and check the consistency. If needed, add in another tablespoon of milk to thin the glaze.

Once the donuts are cool, dunk them face down into the glaze mixture about halfway up the donut, then twist and lift the donut up and out of the glaze.

Let the excess drip off a bit, then turn face up and set onto a cooling rack. Add sprinkles if desired. Let the donuts set up for about 10 minutes so that the glaze firms up just a bit. If the glaze starts to firm up too much while dipping the donuts, heat it in the microwave for about 10 seconds and stir.