Simmer 1 cup of apple cider in a small saucepan over medium heat for approximately 10-12 minutes until reduced to 1/2 cup, then allow to cool.
Preheat oven to 350°F (175°C) and lightly grease a 24-slot mini muffin pan.
In a large mixing bowl, whisk together the flour, 3/4 cup sugar, baking powder, baking soda, 1 teaspoon cinnamon, nutmeg, and salt.
In a medium bowl, whisk together the cooled apple cider reduction, 1/3 cup melted vegan butter, almond milk, applesauce, and vanilla extract.
Fold the wet ingredients into the dry ingredients using a spatula until just combined; do not overmix.
Distribute the batter evenly among the mini muffin slots, filling each approximately 3/4 full.
Bake for 12 to 15 minutes or until a toothpick inserted into the center of a donut hole comes out clean.
In a small bowl, combine the coating sugar and 1 tablespoon cinnamon.
While the donut holes are still warm, brush each with the 1/4 cup melted vegan butter and roll in the cinnamon-sugar mixture until fully coated.