Step 1: Preheat your oven to 350°F (175°C). Lightly grease a 9x13 inch baking dish.
Step 2: In a large bowl, combine the softened cream cheese, sour cream, condensed cream of chicken soup, garlic powder, onion powder, and black pepper. Mix until smooth and well combined.
Step 3: Stir in the cooked, shredded chicken, 1.5 cups of shredded cheddar cheese, and 0.5 cup of shredded Monterey Jack cheese into the creamy mixture. Mix gently until everything is evenly coated.
Step 4: Pour the chicken mixture into the prepared baking dish, spreading it into an even layer.
Step 5: In a separate small bowl, combine the crushed Ritz crackers and melted butter. Stir until the crackers are fully coated.
Step 6: Evenly sprinkle the remaining 0.5 cup of shredded cheddar cheese and 0.5 cup of shredded Monterey Jack cheese over the chicken mixture.
Step 7: Scatter the buttery Ritz cracker topping evenly over the cheese layer.
Step 8: Bake for 25-30 minutes, or until the casserole is bubbly around the edges and the cracker topping is golden brown.
Step 9: Remove from the oven and let the casserole rest for 5-10 minutes before serving. This allows the sauce to set slightly and makes for easier serving.