Bring a large pot of salted water to boil while you cut up the broccoli. I used one head. Cut the florets off, the slice the stems into 1/2" pieces. If the stems are really thick, you can peel them but in the spring mine are generally quite tender.
Blanch the broccoli for 4-5 minutes, until just tender, then scoop out (leaving the water in the pan for the pasta) and drain and rinse with cold water. Plop a few ice cubes on top to cool them off and help retain the nice bright green color.
Put the fettuccine in to cook, about 12 minutes for mine.
Meanwhile... Heat a 1/4 cup or so of olive oil in a saucepan and add a couple cloves of minced garlic. Add some crushed red pepper flakes if you'd like. Cook a few minutes.
Add the broccoli and stir and cook a minute. Now, you could stop here and just pour this over the pasta.
Optionally, add some cream. I added some cream and cook a few minutes to thicken. Pour the sauce and broccoli over the cooked and drained pasta and serve with some grated Parmesan at the table.