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 (350° to 450°F). 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.