Heat oven to 425°F. Line a sheet pan with foil.
Halve poblanos lengthwise and remove seeds. Rub with 1 tbsp oil and a pinch of salt.
Roast peppers cut side down until tender and blistered, 12–15 minutes. Cool slightly.
Warm remaining oil in a skillet over medium heat. Soften onion 3–4 minutes, then stir in garlic.
Season with cumin, chili powder, oregano, salt, and pepper. Cook 30 seconds until fragrant.
Fold in chicken, rice, beans, corn, and tomatoes. Heat, stirring, until hot throughout, 3–4 minutes.
Take off heat. Mix in cream cheese, half the shredded cheese, lime juice, and cilantro until creamy.
Nestle roasted poblanos in a lightly oiled baking dish. Fill each with the warm chicken mixture.
Top with remaining cheese. Bake until melted and bubbly, 10–12 minutes. Broil 1 minute for extra color.
Rest 5 minutes. Garnish with more cilantro and serve with lime wedges if you like.