Preheat your oven to 350˚F. Evenly grease an 8 1/2" by 4/ 1/2” non-stick loaf pan with butter or vegetable oil spray.
Place the cornmeal, flour, sugar, baking powder and salt in a medium bowl and whisk until thoroughly combined. Stir in the cilantro, peppers and cheese.
Beat the egg in a second medium bowl. Mix in the buttermilk and melted butter. Add the wet ingredients to the dry and mix until just combined.
Spoon the batter into the prepared pan. Bake for 45 minutes, or until the loaf springs back when touched gently in the very centre. Cool the loaf in the pan for 15 minutes, then turn it out onto a cutting board. Set the cornbread aside, for now.
Preheat your barbecue until the temperature in the chamber is 375˚F. Brush the outside of the chicken with olive oil. Now sprinkle and rub the bird with the paprika, cumin, chili powder, oregano, salt and pepper. Tuck the wings under the body of the chicken and tie the legs together with kitchen string. Set the chicken in a barbecue-safe skillet, such as a cast iron one.
Set the skillet on one side of the barbecue. Close the lid and turn the heat off underneath the chicken; leave the other side of the barbecue on. Cook the chicken 65 to 75 minutes, or until the temperature in the deepest part of the thigh registers 185˚F on an instant-read meat thermometer. During cooking, brush the chicken occasionally with pan juices, once they start to accumulate in the pan. Also watch the temperature in the chamber and adjust the flame as needed to maintain the 375˚F temperature.
When cooked, remove chicken from the barbecue and let rest 10 minutes before cutting and serving. While the chicken rests, leave the barbecue on and cut the cornbread, widthwise, into 3/4" slices. Lightly oil the bars of grill on the hot side of the barbecue. Grill the cornbread 1 minute per side, or until lightly charred, and then serve with the chicken.