Preheat the oven to 350 degrees. Grease pans with butter or spray with nonstick spray. Whisk flour, baking powder, baking soda, cinnamon, cardamom, nutmeg, cloves and salt in a medium bowl. Set aside.
Whisk sugar, brown sugar, egg, oil, buttermilk, apple compote and vanilla extract in a large bowl until completely smooth. Add dry ingredients and combine with a rubber spatula until the batter just comes together.
Transfer batter to a large Ziploc bag. Cut a small hole in the corner of the bag and pipe the batter into a nonstick donut pan, filling each donut space about three-quarters of the way up with batter.
Transfer to the oven and bake until donuts spring back when touched, about 15 minutes. Set aside to cool slightly.
Meanwhile, make the topping. Combine the sugar, cinnamon, cardamom, nutmeg and cloves in a shallow bowl. When donuts are cool enough to handle, brush each donut with melted butter and toss in sugar and spice mixture until donuts are fully coated. Serve warm.
These are definitely best the day they are made, a bit warm from the oven. If you would like to save some for the next day, wait until you are just about to serve them to brush with melted butter and roll in the sugar and spice mixture.