Reduce the cider. Pour the apple cider into a small saucepan. Bring to a boil, then reduce heat to medium and simmer until the cider has reduced to about ½ cup (10–15 minutes). Set aside to cool slightly.

Prep pans and oven. Heat oven to 350°F (175°C). Lightly grease two 6-cavity donut pans (or a 12-cup muffin tin) with nonstick cooking spray.

Mix dry ingredients. In a medium bowl, whisk together the flour, baking powder, salt, cinnamon, ginger, and nutmeg. Set aside.

Cream butter and sugars. In the bowl of a stand mixer fitted with the paddle attachment, cream together the 10 tablespoons butter, brown sugar, and the ¼ cup granulated sugar on medium speed until light and fluffy, about 3–4 minutes. Add eggs one at a time, mixing well after each addition and scraping down the sides as needed. Beat in the vanilla.

Combine batter. Reduce mixer speed to low and add the dry ingredients until just incorporated. With the mixer running, slowly pour in the reduced cider and mix until smooth, scraping the bowl as needed.

Fill pans and bake. Spoon or pipe the batter into the prepared donut pans, filling each cavity about ⅔ full. Bake 12–15 minutes, rotating halfway, until donuts are lightly golden and a toothpick inserted into the thickest part comes out clean. (For muffins, bake 15–20 minutes.)

Coat with cinnamon sugar. In one small bowl, melt the 6 tablespoons butter. In another, whisk together the raw sugar, granulated sugar, and cinnamon. Let donuts cool in the pan 5 minutes, then turn out onto a rack. Brush each with melted butter and toss in the sugar mixture while still warm.