Preheat oven to 350°F and spray a 9x13-inch baking dish with nonstick spray.
Heat olive oil in a 4-quart Dutch oven over medium-high heat.
Add chopped bell pepper, onion, and celery; cook until onions are translucent and vegetables soften, about 5 to 6 minutes.
Stir in minced garlic and cook for 30 seconds, stirring constantly to prevent burning.
Reduce heat to medium; add cream of chicken soup and half and half, stirring until combined and heated through.
Mix in 2 cups shredded sharp cheddar cheese until fully melted.
Fold in cooked egg noodles and shredded chicken breast, mixing evenly.
Add parsley, salt, and pepper to taste; stir well.
Transfer mixture to the prepared baking dish.
Crush Ritz crackers in a ziplock bag using a rolling pin, then combine with melted butter and 1 cup shredded cheddar cheese in a bowl.
Spread the cracker mixture evenly over the casserole filling.
Bake uncovered for 15 minutes or until topping is golden and cheese is melted.