Cook rotini in a large pot of salted boiling water according to package instructions. Drain.
While the pasta cooks, preheat the oven to 350 degrees F. Spray a 9 x 13-inch baking dish with cooking spray and set aside.
In a large bowl, stir together condensed soups, milk, salt, garlic powder, onion powder and pepper. Add the cooked pasta, ham, broccoli and half of the cheese. Transfer to the prepared baking dish. Sprinkle remaining cheese over top.
In a small bowl, stir together crushed Ritz crackers and melted butter. Sprinkle on top of the casserole.
Bake, uncovered, for about 30 minutes (or until the inside is hot and bubbly and the topping is golden brown).