Preheat oven to 350°F and lightly grease a donut pan.
In a mixing bowl, whisk together flour, sugar, and baking powder. In a separate mixing bowl, whisk together non-dairy milk, vanilla, applesauce, and melted butter. Pour wet ingredients into dry ingredients and whisk until just combined. Pipe or spoon batter into donut pan, filling each about 3/4 full.
Bake for 10–13 minutes, or until set and lightly golden.
Let donuts cool completely before removing from pan.
In a bowl, whisk together powdered sugar, cocoa powder, and vanilla. Add very hot water a tiny bit at a time, whisking until you reach a thick, smooth glaze.
Dip donuts into glaze and let set before serving.