Preheat the broiler.
Make the tahini sauce: Purée one avocado half, garlic, tahini, lemon zest, 5 Tbsp. lemon juice, ⅓ cup mint, 4 Tbsp. oil, and 2 Tbsp. water in a blender, adding a little more water if needed, until smooth. Season with salt and pepper.
Toss broccoli and onion with 2 Tbsp. OLIVE oil; season with salt and pepper. Place on a non-stick lightly oiled baking pan and broil about 6 inches from heat source, turning occasionally, until broccoli crowns are dark brown in places and stems are crisp-tender, 7 - 10 minutes. Let cool slightly.
Coarsely chop broccoli and onion. Toss in a medium bowl with remaining 2 Tbsp. lemon juice and 2 Tbsp. oil; season with salt and pepper.
Spread tahini dressing on a serving platter and top with broccoli mixture. Top broccoli mixture with remaining chopped half of avocado, pine nuts, sesame seeds, drained pepperoncini and more mint.