Start the coals and build a two-zone fire when coals are ready. (Or set your gas grill to medium.) Close the lid and let the grill preheat for about 10 minutes. Make sure the grill grate is clean and seasoned.
Place broccoli florets in a large mixing bowl and drizzle oil and vinegar over the top. Sprinkle salt, garlic powder, black pepper, and lemon zest. Toss broccoli to coat it well in seasonings.
Spread seasoned broccoli florets in a vegetable grilling basket and place on the grill, over direct heat.
Grill broccoli, tossing it every few minutes, for 8-10 minutes. You can cook it a little longer if you want it softer. (If broccoli is charring too much, move it to indirect heat.)
Disclaimer: Nutrition information shown is not guaranteed to be 100% accurate as most ingredients and brands have variations.