While the farfalle is cooking, in a large skillet or pot on high heat add the extra virgin olive oil and garlic and sauté until golden, about 1-2 minutes.
Next, add the broccoli, carrots, salt, and black pepper and sauté for 5 minutes, mixing occasionally.
Next, lower to medium heat and add the diced tomatoes and chicken broth. Bring to a simmer and cook for 5 minutes, mixing occasionally.
Continuing on medium heat add in the cooked pasta and grated cheese and cook for 5 minutes, mixing occasionally to incorporate all of the ingredients.