Apple Cider Donut Muffins

Name: Apple Cider Donut Muffins
Ingredients: 1 1/2 c. apple cider (not juice); 12 tbsp. unsalted butter, room temperature, divided, plus more for pan; 1/3 c. (66 g.) light brown sugar; 1/2 tsp. kosher salt; 1 large egg, room temperature; 1/4 c. neutral oil; 1 1/4 tsp. baking powder; 1/4 tsp. baking soda; 1/4 tsp. ground ginger; 1/4 tsp. ground nutmeg; 4 1/2 tsp. ground cinnamon, divided; 2 c. (240 g.) all-purpose flour; 1/4 c. apple butter (preferably no added sugar); 2/3 c. (133 g.) granulated sugar