Preheat oven to 350 degrees F. Grease a donut baking dish.
In a large bowl mix eggs, sugar, vanilla extract, milk, and butter. Set this aside.
In a small bowl mix flour, cocoa powder, baking powder, baking soda, and salt. Slowly add the dry mix into the large bowl with the wet ingredients.
Pipe (or spoon) the batter into a donut dish. Bake for 8 minutes.
While the donuts are baking, prepare the chocolate glaze by mixing butter, milk, vanilla extract, and chocolate chips on the stovetop until melted and well combined. Mix in the powdered sugar. Remove from heat.
When donuts are out of the oven and cooled, spread the glaze over the top of the donuts and enjoy!