In a medium saucepan over medium-high heat bring the apple cider to a boil and reduce down to 1/2 cup cider. Takes approximately 15-20 minutes to reduce down. Set aside to cool.
In a medium bowl, mix together the flour, baking powder, cinnamon, salt, nutmeg, clove, brown sugar, and can sugar.
In a small bowl whisk together the melted butter, egg, milk rum and cooled reduced cider. Make a well in the center of the dry ingredients and pour in the wet. Mix together until thoroughly combined but do not over mix.
Heat your oven to 350°F and grease a 24 cup mini muffin pan.
Using a small cookie scoop or a tablespoon, scoop the batter into the muffin tin. Each cup should be filled 3/4 high. Bake for 10-11 minutes or until a toothpick inserted in the center comes out clean.
Let cool for about 5 minutes before removing from the tin.
Set up your butter and cinnamon sugar station. Place the butter in a shallow bowl and the cinnamon sugar in a brown paper bag (recommended) or another shallow bowl.
Taking the donuts 3-4 at a time, dip on all sides in the butter and then coat in cinnamon sugar. If using a bag, just place in the bag, seal the top and shake. Remove and set aside to dry. Continue until all the donuts are coated.
Before serving, making the dipping sauce. In a medium saucepan combine the brown sugar, heavy cream, salt and vanilla over medium heat. Bring to a simmer and reduce heat slightly.
Cook for about 2-3 minutes or until the brown sugar is completely dissolved.
Remove from the heat to add the rum and the butter and stir until the butter is completely melted.
Pour the sauce in a heat proof serving bowl and serve hot alongside the donuts.