Preheat and prep: Heat the oven to 400°F (200°C).
Lightly grease a 9x13-inch baking dish. Pat chicken dry with paper towels so it browns better.
Season the chicken: In a large bowl, add chicken strips, 1 tablespoon olive oil, 1/2 teaspoon salt, black pepper, chili powder, cumin, smoked paprika, garlic powder, onion powder, and red pepper flakes if using. Toss until evenly coated.
Arrange the veggies: Add sliced bell peppers and red onion to the baking dish.
Drizzle with remaining 1 tablespoon olive oil and 1/2 teaspoon salt. Toss to coat and spread in an even layer.
Layer the chicken: Place seasoned chicken strips over the peppers and onions. Try not to overlap too much so everything cooks evenly.
Add lime and creaminess: Sprinkle the lime juice over the chicken.
Distribute the cream cheese cubes across the top so they melt into the bake.
Bake: Place the dish in the oven and bake for 18–20 minutes, until the chicken is just cooked through and the peppers are tender-crisp.
Stir in sour cream: Remove the dish and gently stir to melt the cream cheese into the juices and coat everything. Dollop in the sour cream and fold it through. Taste and adjust salt if needed.
Add cheese and finish: Sprinkle the shredded cheeses evenly over the top.
Return to the oven and bake for 6–8 minutes, until the cheese is melted and bubbling with some golden spots.
Garnish and rest: Let the bake rest for 5 minutes so the sauce thickens slightly. Sprinkle cilantro over the top. Serve with lime wedges.