Start by preheating your oven to 350°F (175°C). Grease a standard-sized donut pan and set it aside.
In a medium-sized bowl, mix together the flour, sugar, baking soda, baking powder, and salt. In a separate bowl, combine the egg, yogurt, vegetable oil, milk, and vanilla extract. Carefully pour the wet ingredients into the dry mixture, stirring until just combined. The batter will be a bit lumpy and thick.
Spoon the batter into a large zip lock bag and cut a ½ inch hole in one corner to create an improvised piping bag. Pipe the dough into the donut molds, filling them about ¾ of the way to the top. Bake for 10 minutes. Let them cool in the pan for 5 minutes before coating them with cinnamon sugar.
To make the cinnamon sugar, combine both ingredients in a shallow bowl. Use a small brush to coat each donut with melted butter, then dip each side into the sugar mixture. If you like an extra sugary coating, you can dip each donut twice. Serve and enjoy!