Reduce the apple cider: In a small saucepan, bring the apple cider to a simmer over medium heat. Simmer, stirring occasionally, until it has reduced to 1/4 cup (60g/ml), about 20 minutes. It won’t necessarily be any thicker, but it should be a bit darker. Pour the reduced apple cider into a heat-safe bowl or glass liquid measuring cup, and set aside (or refrigerate to speed things up) to cool to room temperature before using in step 4.

Meanwhile, preheat the oven to 425°F (218°C). Spray a 12-count muffin pan with nonstick spray or use muffin liners. Set aside.

In a large bowl, whisk together the flour, baking powder, baking soda, salt, cinnamon, allspice, cloves, and nutmeg.

In a medium bowl, whisk the oil, brown sugar, granulated sugar, eggs, applesauce, and reduced apple cider until combined. Pour the oil mixture into the flour mixture and whisk until combined. Fold in the shredded apple and chopped walnuts (if using).

Divide the batter evenly among the muffin liners, filling all the way up to the top.

Bake for 5 minutes at 425°F. Reduce the oven temperature to 350°F (177°C). Continue to bake until a toothpick inserted in the center comes out clean, about 15–16 minutes more. Cool the muffins in the pan set on a cooling rack for 10 minutes, then transfer the muffins from the pan to the rack.

Whisk the sugar and cinnamon together in a medium bowl. Lightly brush the top of a warm muffin with melted butter then dip the top into the cinnamon-sugar. Peel off the liner and roll the entire muffin in the cinnamon-sugar to fully coat. (Or coat just the tops.)

Cover lightly and store at room temperature for up to 3 days or in the refrigerator for up to 1 week. The sugared coating draws out moisture, so the muffins become a bit sticky by day 2.