Bring 4 quarts of salted water to a boil and drop in the shrimp. Wait 1 minute; empty the pot into a colander set in the sink. Let the shrimp cool in the colander.
Bring a second pot of salted water to a boil and drop in the broccoli florets. Cook until the stems are just tender, 3 to 5 minutes; do not overcook. Remove the florets from the water with a slotted