Heat oil in a large skillet over medium-high heat. Sautee the chorizo for about 5 minutes, gently breaking it up with a wooden spoon. Stir in the onions, black beans, and garlic. Cook for 2-3 more minutes. Then, mix in the tomato paste, oregano, and cumin. Transfer to a large bowl.

Add rice, tomatoes, sour cream, cilantro, cotija cheese, and 1/2 cup of the jack cheese to the bowl with the meat mixture and mix until combined. Season with salt and pepper to taste.

Slice the poblano peppers lengthwise on one side to create a slit. Gently remove the seeds, and then spoon the mixture into the cavities of the split poblanos and place them on a baking sheet, split side up. Pull the pepper up around the filling and press gently to help it keep its shape. Top with remaining cheese.

Put peppers under the broiler for 2-3 minutes, or until cheese is completely melted. Sprinkle with additional cilantro and serve.