Chop broccoli and broccolini into smaller individual pieces (but not so small that they will fall through the grill grates).
In a small bowl, whisk olive oil, balsamic vinegar, garlic, crushed red pepper, salt and pepper together.
Place the broccoli pieces into a dish. Drizzle the dressing over the broccoli and toss to coat. Let it sit to marinate for 20 minutes. Reserve the leftover dressing for basting.
Heat an outdoor BBQ to medium heat. Grill broccoli until fork-tender (around 10 minutes) - flipping them every 2 to 3 minutes and brushing with the reserved dressing as they are grilling so they don't get too dry.
Transfer the broccoli from the grill to a serving dish.
Serve sprinkled with sesame seeds and more crushed red pepper flakes, if desired.