Bring a large pot of water to a boil for the pasta. Salt water and cook pasta to al dente, according to package directions (about 10-12 minutes total, depending on the brand). When the pasta has been cooking a couple of minutes, add broccolini or broccoli to the water and finish cooking everything together, 8 minutes more.
Meanwhile, melt butter in a saucepot over medium heat. Add garlic and cook 2-3 minutes. Whisk in flour and cook 1 minute then whisk in stock and milk. Let sauce thicken to coat the back of a spoon, stir in 2 cups of cheese and season with salt and pepper.