Bring 4 cups water and mung beans to a boil in a pot; cover, reduce heat to medium-low, and simmer until beans are tender, 45 to 60 minutes.
Bring 5 cups water and millet to a boil in a separate pot; cover, reduce heat to medium-low, and simmer until water is absorbed and millet is tender, 10 to 20 minutes.
Heat oil in a skillet over medium heat; cook and stir onion, green bell pepper, celery, carrot, parsley, garlic, ginger, basil, oregano, cumin, curry powder, and cayenne pepper until vegetables are slightly tender, 5 to 10 minutes. Stir tomatoes, salt, and pepper into vegetable mixture.
Mix mung beans, millet, and Cheddar cheese into vegetable mixture; cook and stir until cheese is melted, 2 to 3 minutes.