While the pasta is cooking, in a large skillet on high heat add in the extra virgin olive oil and sauté the garlic until golden, about 2 minutes.
Next, add in the sliced onion and sauté for 2 minutes, mixing occasionally. Next, add in the sausage and sauté for 5 minutes, mixing occasionally.
Continuing on medium heat add in the broccoli and vegetable stock and cook for 5 minutes, mixing occasionally.
Finally, add in the cooked farfalle and red pepper flakes and cook for 2 more minutes, mixing occasionally to incorporate all of the ingredients.
Place the pasta with sausage and broccoli in a large serving bowl and sprinkle with grated cheese.