Heat the oven to 425 degrees. Coat 2 (6-cavity) doughnut pans with nonstick cooking spray.
Whisk the flour, baking powder, baking soda, cinnamon, and nutmeg in a medium bowl.
Beat the sour cream, brown sugar, butter, oil, and vanilla in a large bowl at medium speed until blended. Add the eggs, one at a time, beating until thoroughly combined. At low speed, slowly beat in the flour (batter will be thick).
Pipe the batter into the pans using a pastry bag and plain tip or a heavy resealable bag with corner cut off filled almost to the top.
Bake for 10 to 12 minutes or until the edges are a pale brown (the bottom will be browner than the top). Cool in the pan for 5 minutes. Remove from the pan and place the doughnuts on a cooling rack.
Top with your favorite toppers. Options: 1) Cinnamon Sugar - Brush the warm doughnuts with melted butter and toss in cinnamon sugar to coat. 2) Glazed - Whisk 1/2 cup sour cream and 2 cups powdered sugar. Dip the doughnuts in the glaze and top with colored sprinkles if desired.