Heat oven to 400°F and grease a 8-inch square baking dish or 8-inch cast iron skillet.
Combine flour, cornmeal, sugar, rosemary, baking powder, baking soda, and salt in a medium bowl. Whisk until evenly mixed
Combine buttermilk, melted butter, and egg in a separate large bowl and whisk until smooth. Add 1 cup of the cheese and the corn and stir just until combined.
Stir in the dry ingredients with a rubber spatula until evenly moistened.
Scrape batter into the prepared pan and bake in the middle rack for 20 minutes. Remove from oven and sprinkle small rosemary sprigs and remaining cheese over the top. Continue baking until the cheese is melted and a toothpick inserted in the center comes out clean, about 10 minutes more.
Let the cornbread cool about 10 minutes then slice and serve with butter and honey.