Preheat the oven to 350 degrees. Spray a regular donut pan with non-stick cooking spray.
In a large bowl, combine butter, oil, sugar, eggs, and vanilla. Stir in milk and yogurt. Whisk until smooth. In a separate bowl, combine flour, baking powder, baking soda, cinnamon, nutmeg, and salt. Add to wet ingredients and stir until fully incorporated.
Divide the batter among 16 donut cavities, filling ¾ of the way full.
Bake for 12-14 minutes, until firm to the touch or passes the toothpick test (a toothpick inserted comes out clean).
Allow to cool in the pan for 10 minutes. Remove the donuts from the pan and place on a cooling rack.
While the donuts finish cooling, melt butter. Combine additional cinnamon and sugar in a shallow bowl.
When cool, brush finished donuts with butter, one at a time. Dip donuts into the cinnamon and sugar mixture immediately following the butter. Continue until all donuts are covered.