Preheat your oven to 350°F (175°C) and lightly grease a muffin tin.
In a small saucepan, bring the apple cider to a boil. Reduce heat and let it simmer until the liquid has reduced to about ½ cup, roughly 10-15 minutes. Set aside to cool.
In a mixing bowl, whisk together the flour, baking powder, baking soda, salt, cinnamon, and nutmeg.
In a separate large bowl, beat together the sugar and eggs until light and fluffy. Slowly incorporate the cooled apple cider, applesauce, vegetable oil, and vanilla extract, mixing until well combined.
Gradually add the dry ingredients to the wet mixture, stirring until just combined. Avoid over-mixing.
Fill each muffin cup about two-thirds full with the batter and smooth the tops.
Bake in the preheated oven for 18-20 minutes or until a toothpick inserted in the center comes out clean.
While the muffins are baking, mix the extra ½ cup of sugar and 1 teaspoon of cinnamon in a shallow dish for coating.
Once the muffins are done, remove them from the oven and let them cool in the pan for 5 minutes. Transfer them to a wire rack.
While still warm, roll each muffin in the cinnamon-sugar mixture until fully coated.
Notes
Arrange the doughnut muffins on a beautiful platter, and sprinkle some extra cinnamon-sugar over the top for a charming finish. Consider serving them alongside a small bowl of apple slices for added freshness!