This cornbread tastes best when served on the same day it's baked.
Preheat oven to 400 degrees. Butter a 9-by-13-inch baking pan. In a bowl, whisk together cornmeal, flour, sugar, baking powder, baking soda, and salt. In another bowl, whisk together buttermilk, butter, and eggs.
Pour buttermilk mixture into flour mixture and stir until just combined (do not overmix). Fold in cheese and chiles with juices until evenly distributed. Transfer to baking pan and smooth top. Scatter pepper rounds evenly over top.
Bake until golden brown along edges and a tester inserted in center comes out with moist crumbs, 20 to 25 minutes.
Let cool in pan 5 minutes. Turn out onto a wire rack, then invert onto another rack, top-side up. Let cool at least 15 minutes more. Transfer to a cutting board. Cut in half lengthwise, then slice each half into small wedges. Serve warm or room temperature.