Place a 10-inch cast-iron skillet into a cold oven and preheat it to 400 degrees.
In the work bowl of your food processor, mix together the cornmeal, all-purpose flour, roasted beets, baking powder, and salt. Blend until beets are completely incorporated into the flour and the mixture has taken on a pink hue. In a medium bowl, mix together the cheddar, pepper, melted butter, honey, eggs, milk, and yogurt and whisk.
Next, add the dry ingredients to the wet ingredients. Stir until just incorporated.
Using a sturdy, reliable oven mitt, carefully remove the hot cast-iron skillet from the oven and place it onto a trivet.
Place the remaining tablespoon of butter into the skillet and swirl it or use a silicone brush to coat the bottom of the pan.
Pour the batter into the pan and place the pan into the oven for twenty to twenty-five minutes.
Run a knife around the edge and turn the cornbread out onto a cutting board.