In a large skillet over medium heat, heat oil. Add onion and cook until soft, 5 minutes. Add garlic, oregano, and cumin and cook until fragrant, 1 minute.
Put grated cauliflower in a clean dishtowel and twist to drain excess liquid.
Add a splash more oil to skillet if it seems dry, then add drained grated cauliflower and season with salt and pepper. Cook, stirring occasionally, until tender, 3 to 5 minutes, then add tomato paste and stir until combined. Stir in chicken, black beans, corn, tomatoes, jalapeños, and cilantro.
Top with cheeses and cover with lid to let melt, 2 minutes.
Serve with limes.
