While the pasta is cooking, in a large skillet, add the extra virgin olive oil and bring to a high heat. Next, add the garlic and onion and sauté for 2 minutes, mixing occasionally.
Next, add the carrots and green beans and sauté for 8 minutes, mixing occasionally.
Lower to a medium heat, add the diced tomatoes, salt, and ground black pepper and cook for 5 minutes, mixing occasionally.
Add in the pasta water and bring to a simmer. Cook for 3 minutes, mixing occasionally. Finally, add in the pasta and cook for 2 minutes, mixing occasionally.
Place the pasta with green beans and carrots in a large serving bowl. Add some grated cheese for more flavor.