Preheat your oven to 350°F (175°C).
In a large mixing bowl, combine cooked rice, diced ham, shredded cheddar cheese, cream of mushroom soup, and milk. Stir until evenly mixed.
Add frozen peas, black pepper, garlic powder, and onion powder to the mixture. Stir well until all ingredients are incorporated.
Pour the mixture into a greased 9x13 inch baking dish, spreading it out evenly.
If desired, sprinkle breadcrumbs over the top for a crunchy texture.
Cover the dish with aluminum foil and bake in the preheated oven for 25 minutes.
After 25 minutes, remove the foil and continue baking for an additional 15-20 minutes, or until the top is golden and the cheese is bubbly.
Remove from the oven and let it rest for 5-10 minutes before serving.