Heat olive oil in a large pot over high heat. Add ground beef, onion, and salt. Cook and stir with a wooden spoon or spatula until meat is browned and crumbled into small pieces, about 5 minutes. Stir in flour and cook for 2 minutes. Add poblano pepper, garlic, chili powder, cumin, black pepper, cayenne, and oregano; cook, stirring, for 2 to 3 minutes.

Stir in diced tomatoes and crushed tomatoes. Measure water using the empty tomato cans and pour into the pot. Bring to a simmer, stirring occasionally, then reduce heat to medium-low. Let simmer, stirring occasionally, for 30 minutes before stirring in kidney beans. Continue simmering until bubbling and fragrant, about 30 minutes more. Taste for seasoning and adjust.

Preheat the oven to 400 degrees F (200 degrees C).

Place a deep 9x13-inch baking dish on a baking sheet. Transfer chili to the dish, being sure to leave at least 1 inch of space at the top. Stir to evenly distribute.

Make crust: Whisk together corn muffin mix, 1/2 cup Cheddar cheese, milk, and eggs in a large bowl until smooth. Spoon batter evenly over chili until the surface is covered. Sprinkle with remaining 1/2 cup Cheddar cheese.

Bake in the preheated oven until cornbread crust is browned and a toothpick inserted into crust comes out clean, about 30 minutes.

Spoon or ladle into a dish and garnish with sour cream and cilantro.