Preheat oven to 375 degrees. In a large bowl, combine flour, baking powder, baking soda, caraway seeds salt, and pepper. In another bowl, whisk together melted butter, egg, and buttermilk, then add shredded cheese and diced ham.
Stir the wet mixture into the dry mixture just until moistened being careful to not over stir.
Spoon batter into greased muffin tins and bake for 25-30 minutes or until cooked through.