Preheat your oven to 350°F (175° C). Grease a 6-cup doughnut pan with melted butter or spray with a cooking spray. Alternatively, you can use a 12-cup muffin pan.
Whisk together the melted butter, yogurt, milk,egg, vanilla and sugar in a large bowl until combined.
Add the flour, baking soda, baking powder, and salt and mix just until combined. Stir in the blueberry jam and fresh/frozen blueberries only 2-3 times to have only streaks of jam.
Transfer the batter into a piping bag, pipe it into each doughnut cup (filling 2/3 the way full). Bake in the preheated oven for 10 minutes. Remove from the oven and allow to cool for 5 minutes. Place the doughnuts onto a cooling rack. You might need to run a knife around the edges to release them. Repeat with the remaining batter.
In a shallow bowl mix the cinnamon and sugar.
Brush each doughnut with melted butter and dip into the cinnamon-sugar mixture. Enjoy!
Notes
If using a muffin pan, fill 2/3 the way full. Bake for 12 minutes or until a toothpick inserted into the middle of a muffin comes out dry, not with wet batter.