How to Make It
Preheat oven to 375°F. Cut 3 cheese slices into 4 squares each (12 total squares). Chop remaining 5 cheese slices; set aside.
Whisk together flour, cornmeal, baking powder, sugar, salt, and pepper in a large bowl. Whisk together buttermilk, melted butter, and eggs in a second large bowl until smooth. Add flour mixture to buttermilk mixture, stirring until just combined. Stir in chopped cheese, 1 cup ham, and 1/2 cup scallions.
Coat a 12-cup muffin pan with cooking spray. Spoon 1/2 cup batter into each muffin cup. Bake until muffins rise and appear dry on top, 10 to 12 minutes.
Place 1 cheese square on each muffin, and top evenly with remaining 1/2 cup shredded ham. Bake until a toothpick inserted comes out with moist crumbs, 8 to 10 minutes. Sprinkle muffins with remaining 1 tablespoon scallions. Let cool in pan on a cooling rack 10 minutes before removing muffins, using a butter knife to loosen edges from pan.