In a large skillet over medium heat, heat oil. Add onion and cook until tender, about 5 minutes. Stir in garlic, oregano, and cumin and cook until fragrant, about 1 minute.
Add more olive oil if the skillet seems dry, then add cauliflower rice. Season with salt and pepper and cook, stirring occasionally, until rice is tender, 3 to 5 minutes.
Add tomato paste and stir until evenly combined and the cauli rice is slightly red. Add chicken, black beans, corn, tomatoes, jalapeños, cilantro and stir until evenly combined.
Top cauli rice with both cheeses, then cover with a tight-fitting lid and cook until cheese is melted, about 3 minutes.
Serve immediately with lime wedges.