Bring a large pot of lightly salted water to a rolling boil. Stir in egg noodles and return to a boil. Cook the noodles uncovered, stirring occasionally, until cooked through but still slightly firm, about 5 minutes. Drain well.
Sprinkle both sides of chicken breasts with salt and seasoned salt.
Heat vegetable oil in a large skillet over medium heat and cook chicken breast halves in the hot oil until browned and no longer pink in the middle, 5 to 8 minutes per side. Set chicken breasts aside.
Mix cream of mushroom and cream of chicken soups, Cheddar cheese, mushrooms, and garlic in a large bowl.
Spread noodles in an even layer into the bottom of an 8x8-inch baking dish.
Arrange asparagus spears in a layer over the noodles.
Dice chicken breasts and spread over the asparagus spears.
Pour soup mixture over the asparagus.
Sprinkle cracker crumbs evenly over the casserole; drizzle melted butter over the crumbs.
Cover the dish and bake in the preheated oven for 15 minutes.
Remove the cover and bake until the casserole is bubbling and the crumbs are browned, about 15 more minutes. Allow to stand 10 minutes before serving.
