Prepare the chili: Preheat the oven to 425 F degrees. In a 12-inch cast-iron skillet, heat the olive oil until it shimmers. Add the ground meat and season with salt and pepper. Cook over medium-high heat, breaking up the meat with a wooden spoon, until just starting to brown but not cooked through, about 5 minutes.
Add the onions, poblanos, jalapeños, garlic and a pinch each of salt and pepper to the skillet. Cook over medium heat, stirring occasionally, until the vegetables are just softened and the meat is cooked through, 6 to 8 minutes. Add the chili powder and cumin and cook, stirring, until fragrant, about 30 seconds. Stir in the enchilada sauce and chicken broth and bring to a boil. Simmer, over medium-low heat, stirring occasionally, until slightly thickened, about 5 minutes. Stir in the beans and/or corn kernels and remove from heat.
Meanwhile, prepare the cornbread: In a medium bowl, whisk the masa harina with the flour, baking powder, salt and pepper. In another medium bowl, beat the eggs with the milk and chicken broth. Add the wet ingredients to the dry and whisk the batter until smooth. Fold in 1/4 cup of the cheese.
Dollop the cornbread batter over the chili and gently spread into an even layer. It will seem like a very thin layer of cornbread, but it will rise in the oven. Scatter the pickled or regular jalapeños over the batter, then sprinkle the remaining 1/4 cup of cheese on top. Bake the tamale pie until bubbling and the cornbread is risen, 25 to 30 minutes. Remove from the oven and let it sit for 5 minutes before serving. Serve with hot sauce and sour cream.