Heat oven to 350°F. Grease a donut pan.
Whisk the flour, ½ cup sugar, baking powder, baking soda, cinnamon, nutmeg, and salt in a large bowl.
In a second bowl, whisk the apple cider, applesauce, egg, oil, and vanilla. Fold into the dry ingredients until just combined.
Fill each donut cavity ¾ full. Bake 10–12 minutes, until springy to the touch. Cool 5 minutes, then pop out of the pan.
Brush each donut with melted butter and toss in the cinnamon-sugar (½ cup sugar + 1 tsp cinnamon).
Drizzle with warm caramel and serve!