Prepare Cider: Pour apple cider into a saucepan and heat over medium heat. Simmer for about 30 minutes, stirring occasionally, until thickened. Remove from heat and cool slightly.

Mix Dry Ingredients: In a mixing bowl, whisk together flour, baking powder, cinnamon, nutmeg, and salt until blended. Set aside.

Combine Wet Ingredients: In another bowl, beat sugar and softened butter until creamy. Add egg and mix until incorporated. Stir in cooled cider and vanilla until smooth.

Combine Mixtures: Slowly fold dry ingredients into wet ingredients until just combined. Let dough rest for about 10 minutes.

Shape Donuts: Lightly flour countertop, roll dough to 1/2 inch thick, and cut out shapes using a donut cutter. Place on a floured baking sheet.

Fry Donuts: Heat oil to 350°F. Fry donuts for 2-3 minutes on each side until golden brown. Drain on paper towels.

Coat in Cinnamon Sugar: Mix sugar and cinnamon in a bowl. Toss warm donuts in the mixture to coat.

Cool and Serve: Place coated donuts on a wire rack to cool slightly. Serve warm for the best experience.