In a medium to large bowl, whisk together the dry ingredients: flour, sugar, cocoa, baking soda, and salt. In a smaller, separate bowl, stir together the wet ingredients: milk, oil, vinegar, and vanilla.
Stir the wet ingredients in with the dry until no lumps remain. Lightly butter or spray the donut baking pan before spooning the batter in.
Bake at 350°F for 14-15 minutes. Remove from the oven and allow to cool in the pan before turning out onto a cooling rack.
For the glaze, in a medium pot over medium heat, melt the butter and stir in the cream or milk, corn syrup, and vanilla. Add the chocolate chips, turning the heat down slightly if needed, and continue to cook and stir until the chips are melted.
Remove the pot from the heat and whisk in the powdered sugar. You may want to shift the sugar first, to remove any lumps, so your glaze will be lump-free.
Dip the donuts in the still-warm glaze, tapping off any extra. Then, top with sprinkles if using.