Preheat a charcoal or gas grill to medium-high (about 425 degrees F).
Place the broccoli in a large bowl. Top with the olive oil, vinegar, maple syrup, salt, and red pepper flakes. Toss to coat.
Coat either a large grill basket or a large sheet of aluminum foil with nonstick spray. Place the broccoli in a single layer in the basket or place the foil on the grill and spread the broccoli onto it in a single layer. Grill for 10 to 13 minutes with the lid closed, tossing once or twice throughout, until the broccoli is lightly charred and crisp-tender.
Transfer to a serving plate (or serve it right off of the foil or grill basket). Sprinkle with Parmesan and season with a pinch of additional salt to taste. Enjoy!
Notes
TO STORE: Refrigerate broccoli in an airtight storage container for up to 4 days.
TO REHEAT: Rewarm leftovers on a baking sheet in the oven at 350 degrees F.
TO FREEZE: Freeze broccoli in an airtight freezer-safe storage container for up to 3 months. Let thaw overnight in the refrigerator before reheating. Note that broccoli that has been frozen will be more mushy.