Preheat oven to 350 F. Grease a mini-muffin tin.
In a large mixing bowl, whisk together flour, baking powder, salt, nutmeg and cinnamon.
In a small bowl, whisk together sugar, oil, egg, vanilla extract, and buttermilk.
Stir wet ingredients into flour mixture until just moistened.
Spoon batter to fill each muffin cup halfway full.
Use a piping bag with a 1/4 inch round tip, or a small spoon to add 1/2 tsp of jam into each muffin cup.
Cover jam with enough donut batter to fill muffin cups almost all the way to the top.
Bake 5-10 minutes until golden brown.
While the muffins are baking, make the topping. Put the butter in a small bowl and melt in the microwave in short bursts. Stir the cinnamon and sugar together in a separate bowl.
Remove the muffins from the oven and let cool 5 minutes. Using tongs, remove the muffins from the pan and dip in the melted butter, and then in the cinnamon sugar mixture.
Let the muffins cool on a wire rack. For best results, eat the warm doughnuts immediately.