Heat the olive oil in a large skillet or pot over medium heat. Add the chopped onion, bell pepper, and carrots, cooking until softened—about six minutes while stirring occasionally.
Stir in minced garlic, chili powder, ground cumin, and salt to the pan with your sautéed vegetables. Cook for about 30 seconds until fragrant.
Incorporate diced tomatoes, diced tomatoes with green chilies, elbow macaroni, black beans, kidney beans, and water into the mixture in your pot. Stir well to combine all ingredients thoroughly.
Increase heat to medium-high to bring everything to a simmer. Once simmering, reduce heat to low, cover the pot, and cook while stirring occasionally until pasta is tender—about twelve to fifteen minutes.
Remove your pan from heat once cooked through. Stir in most of the shredded cheese, leaving some aside for topping later on; then sprinkle remaining cheese on top before serving.