Pour apple cider into a medium saucepan and bring to a boil over high heat. Cook, without stirring, until reduced to about 1/2 cup, 12 to 15 minutes. Remove from heat and set aside.
While cider reduces, preheat the oven to 350 degrees F (175 degrees C). Generously rub shortening all over the inside of a 12-cup Bundt pan. Sprinkle some flour all over inside of pan over shortening and tap around to completely cover in flour. Tap out excess flour and set pan aside.

Whisk together flour, baking powder, baking soda, salt, nutmeg, cloves, and 2 teaspoons of the cinnamon in a medium bowl.

Whisk together eggs, brown sugar, oil, buttermilk, apple butter, vanilla, 2/3 cup of the granulated sugar, and reduced apple cider in a large bowl. Add half of flour mixture to egg mixture and stir to combine. Add remaining half of flour mixture and grated apple and stir until just incorporated, but some lumps still remain, and making sure apples are evenly incorporated (you may need to use a fork to separate apple pieces). Pour into the prepared pan.
Bake in the preheated oven until golden brown and a toothpick inserted in center of cake comes out clean, 50 to 55 minutes. Cool cake in the pan on a wire rack for 15 minutes. Remove cake from pan to a wire rack to cool completely, about 1 hour.
Stir together remaining 1/3 cup granulated sugar and 1 1/2 teaspoons cinnamon in a small bowl. Brush melted butter evenly over outside and center ring of cake. Sprinkle top and sides of cake with cinnamon-sugar.