Preheat the oven to 350°F (175°C) and lightly spray one or more donut pans with nonstick cooking spray.
In a medium bowl, whisk together the flour, 1/4 cup (20 g) unsweetened cocoa powder, baking soda, salt, and 1/2 cup (100 g) granulated sugar until evenly combined.
In a separate bowl or large measuring cup, whisk the 1/2 cup milk, egg, 2 tablespoons (30 ml) vegetable oil, and 1 teaspoon vanilla extract until smooth.
Pour the wet ingredients into the dry ingredients and whisk until just combined and no large lumps remain.
Transfer the batter to a gallon-size resealable bag or piping bag, snip off one corner to make a 1/2-inch opening, and pipe the batter into the prepared donut pan cavities about three-quarters full.
Bake for 7–8 minutes, or until a toothpick inserted into a donut comes out clean. Let the donuts cool in the pan about 10 minutes, then gently remove them to a wire rack or flat surface to cool completely before topping.
To make the chocolate glaze: whisk 1 cup (113 g) powdered sugar with 3 tablespoons (15 g) unsweetened cocoa powder, then whisk in 2 tablespoons milk and 1 teaspoon corn syrup a little at a time until smooth and pourable.
Dip each cooled donut upside down into the glaze, set glaze side up on a baking sheet or flat surface, and sprinkle with optional sprinkles. Let the glaze set about 20 minutes.
To make the cinnamon-sugar topping: whisk 1 cup (200 g) granulated sugar and 2 tablespoons ground cinnamon in a medium bowl. Dip each donut in melted butter, then dredge in the cinnamon-sugar, and if desired give a second light dusting.
Serve once the glaze or cinnamon sugar has set.