Preheat your oven to 375°F (190°C) and line a 12-cup muffin pan with paper liners or grease lightly.
In a large mixing bowl, combine the all-purpose flour, baking powder, cinnamon, nutmeg, and salt. Whisk together to blend.
In a separate bowl, whisk together the brown sugar, granulated sugar, vegetable oil, egg, vanilla extract, apple cider, and applesauce until smooth.
Gradually pour the wet ingredients into the dry ingredients, stirring gently until just combined. Be careful not to overmix; it’s okay if a few lumps remain.
Fold in the shredded apple and nuts, if using, until evenly distributed throughout the batter.
Divide the batter evenly among the muffin cups, filling each about 2/3 full.
Bake in the preheated oven for 15-20 minutes, or until a toothpick inserted in the center comes out clean.
Allow the muffins to cool in the pan for 5-7 minutes before transferring them to a wire rack to cool completely.