Fill a large saucepan with water to within a few inches of the top. Add
2 teaspoons of the salt to the water and bring to a boil over high
heat. Add the broccoli to the boiling water and cook until bright green
and crisp-tender, 3 to 5 minutes. Remove from the saucepan and plunge
into an ice bath to rapidly cool them. Then remove the broccoli from
the ice bath and drain.
Prepare the grill for direct cooking over medium heat. Brush the
cooking grates clean. Preheat a grill pan over direct medium heat for
about 10 minutes.
In a large bowl mix the broccoli, oil, lemon zest, and the remaining ½
teaspoon salt.
Spread the broccoli on the grill pan in a single layer. Grill over
direct medium heat, with the lid closed as much as possible, until the
broccoli is warm and just begins to brown, 4 to 6 minutes, turning
occasionally.
Remove from the grill and garnish with the cheese. Serve warm.