For the batter: Preheat the oven to 375 degrees F and place an 8- to 10-inch cast-iron skillet inside.
Combine the cornmeal, masa and salt in a large mixing bowl. Place the butter in a small saucepot over medium heat. When the butter is melted, remove the pan from the heat and whisk in the milk and eggs. Add all of the liquid to the dry ingredients. Stir with a wooden spoon or spatula until the batter just comes together (a few lumps are okay). Set the batter aside to rest.
For the filling: Melt the butter in a large saute pan over high heat. Add the onions, garlic and peppers and cook, stirring occasionally, until slightly softened, about 5 minutes. Add the chicken and sauce to the pan and bring to a simmer. Remove the pan from the heat and stir in the cilantro, lime zest and juice and Cheddar.
Transfer the filling to the preheated cast-iron skillet, then pour the batter over the top. Bake until the top is risen and browned, and a knife inserted into the center comes out clean, about 30 minutes. Cool on a rack 5 to 10 minutes before serving. Serve with sour cream.
Preheat the oven to 375 degrees F.
In a small bowl, mix together the coriander, smoked paprika, cumin. 1 tablespoon salt and 1 teaspoon ground black pepper.
Lightly coat the chickens with oil, then sprinkle generously with the salt and spice mixture.
Combine the tomatoes, garlic and onions in a large roasting pan and place the two chickens on top, breast-side up. Roast until an instant-read thermometer inserted in the thigh registers 160 degrees F, about 45 minutes (as the chicken rests, the temperature will rise to 165 degrees F).
Transfer the chicken to a large carving board to rest, then place the roasting pan on the stovetop and bring the tomato mixture to a boil. Boil for 1 minute and season to taste with salt and pepper. Puree with a hand blender or transfer to a blender to process until smooth. Reserve the sauce and serve the chicken.
After serving the chicken, pull any remaining meat from the bones and mix with the sauce. Freeze in small containers for up to 3 months.