Preheat the oven to 350 degrees F. Spray a mini muffin pan with nonstick spray.
In a medium bowl, use an electric mixer to combine the butter and sugar until fluffy. Add the egg, milk and vanilla and mix to combine.
In a separate bowl, whisk together the flour, baking powder, cream of tartar, cinnamon and salt.
Add the flour mixture to the egg mixture a little at a time. Mix just until the flour mixture is incorporated. Don't overmix.
Fill each muffin tin 3/4 full. Bake for 9 to 11 minutes. If you're making regular-sized muffins, bake 14 to 16 minutes.
In a small bowl, combine the sugar and cinnamon. Remove the muffins from the tin. Dip the tops of the muffins in the melted butter and roll the tops in the cinnamon-sugar mixture. These are best served warm.