Preheat the oven to 350 degrees F (175 degrees C). Grease donut pans well.
Sift flour, sugar, cocoa, baking powder, and salt together into a large bowl.
Whisk milk, egg, butter, oil, and 2 teaspoons vanilla extract together in a small bowl. Stir into flour mixture until just combined.
Spoon batter into the prepared donut pans, filling each well 3/4 full.
Bake in the preheated oven until a toothpick inserted into a donut comes out clean, about 10 minutes. Remove from the oven and let cool for about 5 minutes; tap donuts out onto a sheet pan.
Combine confectioners’ sugar, hot water, and remaining vanilla extract in a bowl to make the glaze.
Place parchment paper under a wire cooling rack. Transfer cooled donuts to the rack and coat in glaze, letting excess drip onto parchment paper; coat the donuts a second time if desired.
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