Step 1. Heat oven to 200°F and place a baking sheet on an oven rack. In a large bowl, mix cornmeal, flour, baking powder, baking soda, and salt until combined.
Step 2. In a medium bowl, whisk honey, eggs, buttermilk, and butter. Pour mixture into dry ingredients and stir quickly yet strongly until just combined. Fold in cheese.
Step 3. Heat a large skillet or griddle over medium heat and grease thinly with butter. When butter is hot, pour out as many 4-ounce pancakes as your skillet will hold without overcrowding (3 to 4 at a time in a 13-inch pan). Cook for 3 to 5 minutes, or until batter is bubbling and pancakes are browning at the edges. Flip, and cook for another 3 to 5 minutes. Transfer to the baking sheet in the oven, and repeat until all batter is used. Serve hot.