Make the Reduced Apple Cider 

1. Combine cider, brown sugar, and cinnamon sticks in a medium saucepan.
2. Bring to a gentle boil, then simmer until reduced to about 1¼ cups (300 ml) (25–30 min).
3. Remove cinnamon sticks and cool completely.

Bake the Apple Cakes

1. Preheat the oven to 350 °F (175 °C). Line three 8-inch pans with parchment and grease well.
2. In a large bowl, whisk flour, baking powder, baking soda, salt, cinnamon, nutmeg, and cloves.
3. In another bowl, whisk brown sugar, granulated sugar, and oil until smooth.
4. Whisk in eggs one at a time, then applesauce, vanilla, and ½ cup (120 ml) cooled cider reduction.
5. Fold in dry ingredients in two additions until just combined—do not overmix.
6. Divide evenly among pans and smooth tops.
7. Bake for 30–40 minutes, until a toothpick inserted in the center comes out clean.
8. Cool 10–15 minutes in pans, then turn out onto wire racks.

Coat with Cinnamon Sugar

1. Stir together 1 cup sugar and 1 tbsp cinnamon in a shallow dish wide enough for an 8-inch cake layer.
2. When the cakes are cooled enough to handle, brush on all sides with the remaining cider reduction. Dip or gently press each layer into the cinnamon-sugar until evenly coated (or sprinkle and press if layers feel delicate).
3. Cool completely before frosting.

Make the Icing & Assemble

1. In a stand mixer with the paddle attachment, beat butter and brown sugar on medium speed until light and smooth, 2–3 minutes.
2. Add softened cream cheese and beat 1–2 minutes until fluffy.
3. Add powdered sugar, vanilla, and salt. Mix on low until incorporated, then beat on high until airy, 4&