Heat oven to 400°F and grease a 8-inch square baking dish or 8-inch cast iron skillet.
Combine 1 cup flour, 3/4 cup cornmeal, 1/4 cup sugar, 1 tablespoon chopped rosemary, 1 teaspoon baking powder, 1 teaspoon baking soda, and 1/2 teaspoon salt in a medium bowl. Whisk until evenly mixed
Combine 1 cup buttermilk, 1/2 cup melted butter, and 1 egg in a separate large bowl and whisk until smooth. Add 1 cup of the cheese and the 1 cup 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 1/4 cup 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.