Preheat oven to 350°F. Grease a 24-count mini muffin pan with non-stick cooking spray. Set aside.
In a medium bowl, combine the flour, baking powder, baking soda, salt, and cinnamon. Set aside.
In a large bowl, cream butter and sugar with an electric hand mixer or stand mixer with fitted paddle attached until light and fluffy, about 3-4 minutes.
Add in egg, milk, yogurt, and vanilla. Mix until combined.
Add dry ingredients into wet ingredients and incorporate until just combined. Be careful not to over-mix, as that will result in a denser donut.
Spoon mixture in a large ziplock bag and cut the tip of the bottom corner. Pipe filling into each muffin cavity, filling 3/4 full. Alternatively, you can spoon batter into each muffin cavity, filling 3/4 full.
Bake for 9-11 minutes, or until a toothpick inserted into the center of a donut comes out clean. Remove from oven and let cool in pan for 5 minutes, then remove to a wire rack to cool completely.
Once donut holes are completely cooled, make the cinnamon sugar mixture. Pour melted butter into a small bowl and set aside.
In another small bowl, combine the white sugar and cinnamon. Working one at a time, take each donut hole, dip completely into melted butter, and then roll in cinnamon sugar mixture, ensuring that the entire donut hole is coated. Repeat until all donut holes are coated in mixture.