Preheat the oven to 350°F and lightly grease two 6-count donut pans or one 12-count donut pan.
In a medium bowl, whisk together the flour, cocoa powder, baking powder, salt, and nutmeg.
In a large bowl, whisk the sugar, eggs, and vanilla extract until smooth.
Add the oil and melted butter to the wet mixture and whisk again.
Pour in the milk and whisk until incorporated.
Add the dry ingredients into the wet ingredients and whisk until smooth and combined. Avoid overmixing.
Transfer the batter into a large zip-top bag and snip off one corner.
Pipe the batter into the prepared donut pans, filling each cavity nearly full.
Bake the Chocolate Glazed Donuts for 10 to 10½ minutes or until baked through.
Let the donuts cool in the pans for 3 to 5 minutes before transferring them to a wire rack.
To make the glaze, whisk together powdered sugar, cocoa powder, milk, vanilla extract, and corn syrup until glossy and smooth.
Dip each cooled donut into the chocolate glaze, allowing excess glaze to drip off.
Add chocolate sprinkles or toppings while the glaze is still wet.
Allow the glaze to fully set before serving.