Fill a large pot with water and bring to a boil.
Fill a large bowl with ice and water.
While the pot is heating up, wash the broccoli and then carefully slice off the outside "bark" of the stalks. Many people cut the stalks off completely, but they are actually the most fought over piece of the vegetable in my house. The trick is to slice off the outside to expose the heart of the stalk.
Slice each head of broccoli in half, length-wise.
Once the water has come to a boil, carefully place the stalks of broccoli in the boiling water and cook (blanch) for 3 minutes and then immediately submerge the broccoli in the cold water to stop the cooking process.
Place the blanched broccoli in a strainer and allow to dry for a few minutes.
While you wait, fire up that grill for indirect grilling by turning one half of the burners to high and leaving the other burners off. Obviously, if you are using a charcoal grill pile up the coals to one side.
Brush each broccoli stalk with olive oil and then immediately sprinkle with the cheese and a little salt and pepper. I like to sometimes dip the heads of broccoli in the oil and then dip into the cheese to get "snow in the trees".
Place the broccoli on the "off" side of the grill and close the lid.
Let the broccoli roast on the grill for 15 minutes and then test the doneness on one of the heads. Remember, every time you open the lid, you are letting all of the heat out, so keep it closed.
Continue to grill the broccoli with the lid closed until you hit your desired doneness. It usually takes mine 20 minutes, but some people like it more or less crispy.
Serve with the extra cheese.