Preheat the oven to 400°F.
Heat the oil in large deep oven-safe skillet (or 3.5-qt braiser) over medium-high heat.
Add the bell peppers, onions, poblanos, jalapeños, mushrooms, salt, and pepper. Cook, stirring, until the veggies are tender, about 5 minutes.
Add the chicken, garlic, cumin, oregano, and cayenne pepper. Stir to combine. Sprinkle in the cassava flour and stir until well combined, lightly toasting the flour, about 2 minutes.
While stirring, slowly pour in the broth until it is well incorporated. The mixture should be very thick. Reduce the heat to low.
Stir in the can of diced tomatoes and green chiles, green chiles, and yogurt until well combined. Top the corn tortilla strips, lime juice, and 1 cup of shredded cheese. Gently fold into the mixture until well combined. Spread into an even layer and sprinkle the top with the remaining 1 cup of shredded cheese.
Transfer to the oven and bake until the cheese is melty, bubbly, lightly browned, about 20 minutes.
Remove from the oven and let rest for 5 to 10 minutes for the sauce to settle and to cool slightly. Garnish with fresh cilantro, serve, and enjoy!