Heat the olive oil in a large skillet* or pot over medium heat. Add the onion, bell pepper and carrots and cook until softened, stirring occasionally, about 6 minutes.
Add the garlic, chili powder, cumin, and salt to the pan with the vegetables and cook, stirring, for 30 seconds.
Stir in the diced tomatoes, diced tomatoes with green chilies, pasta, black beans, kidney beans and water. Stir.
Increase the heat to medium-high and bring to a simmer. Reduce the heat to a low simmer, cover, and cook, stirring every few minutes, until pasta is tender and most of the liquid has been absorbed, about 12-15 minutes.
Remove the pan from the heat and stir in most of the cheese, reserving a little for sprinkling on top. Sprinkle on the remaining cheese. Serve.