Preheat the oven to 350°F/176°C and spray your donut pan with baking spray. This recipe makes 12 to 15 donuts, so have more pans handy.
Add the cooled melted butter, oil, eggs, vanilla extract, and buttermilk to a mixing bowl and whisk until well combined.
Mix the flour, granulated sugar, baking powder, baking soda, nutmeg, and salt in a large mixing bowl until well combined.
Add the wet ingredients to the dry and mix until smooth and combined, being careful not to overmix the batter. The mixture will be quite thick, but all of the flour should incorporate into the dough. If it seems stiff or dry, add a little more buttermilk.
Pipe the dough evenly into the pans, filling the cavities ¾ full.
Bake for 12 to 14 minutes or until a cake tester comes out clean.
Remove from the oven and let cool for fix minutes before coating.
Melt the butter for the topping and set aside to cool.
To make the cinnamon sugar, combine both ingredients in a small bowl.
Dip each side of the donut into the butter, or use a brush to brush the butter onto the donut. Then dip the buttered donut into the cinnamon mixture until well coated.