Preheat oven to 350 F. Use nonstick cooking spray to grease donut cavities.
Sif the dry ingredients (flour, sugar, cocoa powder, baking powder, baking soda, and salt) into a large bowl. Add the remaining ingredients (milk, eggs, butter, and vanilla extract) and stir to combine.
Transfer batter in a piping bag (if you don't have one, a ziplock plastic bag with the end snipped off will work just fine) and pipe batter into each donut cavity in the greased donut pan, filling no more than 3/4 of the way full. Bake 15 minutes in preheated oven until the chocolate doughnuts spring back when touched. Let cool for 5 minutes in the pan, then flip baked donuts onto a cooling rack.
You should have enough batter for 12 donuts, so repeat with remaining donut batter, if you are using a 6-cavity donut pan.
While the donuts cool, melt the butter and the chocolate chips in a microwave-safe small bowl, blasting in 20 second increments until the chocolate chips just begin to melt. Stir in the syrup and water until you have a thick but liquid consistency. Once fully cooled, dip the tops of the donuts in glaze. Add sprinkles to the top of each donut. Enjoy with a cup of coffee or a glass of milk.
Donuts will keep for several days in an airtight container, but definitely taste best on the first day.