Preheat the oven to 350°F (175°C).
In a large mixing bowl, combine the cooked rice, diced ham, shredded cheddar cheese, frozen mixed vegetables, milk, mayonnaise, garlic powder, onion powder, salt, and pepper.
Transfer the mixture into a greased 9x13 inch baking dish, spreading it out evenly.
Cover the dish with aluminum foil and bake in the preheated oven for 25 minutes.
Remove the foil and bake for an additional 15-20 minutes, or until the top is golden and bubbly.
Let it cool for a few minutes before serving your cheesy rice and ham casserole.