Preheat oven 350 degrees F. Spray one 24-cup or two 12-cup mini muffin tins with baking spray and set aside.
In a medium bowl, whisk together flour, baking powder, salt, cinnamon and nutmeg. In a separate large bowl, whisk together oil, brown sugar, egg, vanilla, banana and milk until smooth. Add dry ingredients to wet ingredients and mix until just combined.
Using a tablespoon or cookie scoop, fill muffin cups 3/4 full. Bake for 10-12 minutes, or until a toothpick comes out clean.
While the muffins bake, melt butter in one bowl and combine granulated sugar and cinnamon in another bowl. Remove muffins from oven and cool for 2 minutes. Dip each muffin in melted butter, then roll in cinnamon sugar to coat.
Serve donut holes warm or at room temperature.
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