Preheat your oven to 400 F with the rack set in the middle and an 8x8 inch baking pan inside.
Whisk flour, cornmeal, baking powder, baking soda, and salt together in a large bowl.
Remove the stems from the rosemary and finely mince it on a cutting board before adding it to the dry ingredients. Whisk once more to evenly distribute the rosemary throughout.
Whisk the milk and yogurt together in a separate bowl. Pour the eggs into the milk mixture and whisk again to combine. Pour the olive oil in and whisk just to combine.
Make a well in the dry ingredients and pour the milk and yogurt mixture into the center. Stir well with a wooden spoon.
Pour the honey into the bowl and stir well. Add most of the cheddar cheese to the batter, making certain to reserve some to go on top, and fold it into the batter.
With pot holders, remove the 8x8 inch baking pan from the oven. Add the butter to the hot pan and tilt the pan to let the butter melt and coat the inside of the pan’s bottom and sides.
Pour the cornbread batter into the pan and lightly tap the bottom on the counter to remove any air bubbles. Sprinkle the rest of the cheddar cheese around the top of the batter and add rosemary flowers on top.
Bake the cornbread for 25-30 minutes or until a toothpick inserted in the middle comes out clean and the top has become a dark golden brown all over.
Remove the cooked cornbread and allow it to cool about 10 minutes before cutting into 12 pieces. Serve warm.