First, sauté the garlic in the butter and olive oil over medium heat for 1-2 minutes. Then add the noodles, stock, milk and broccoli. Bring to boil, cover, and reduce heat to a simmer for 8-9 minutes. Remove the lid and allow to cook for another 8-9 minutes until the liquid has mostly evaporated/absorbed into the noodles and broccoli. Toss in the cheese during this last 8-9 minutes of cooking.