Preheat grill to very high (500°F and up). Cut broccoli into 1/2-inch-thick steaks; lightly brush with canola oil. Place broccoli steaks on oiled grates; grill, uncovered, turning occasionally, until deeply charred in spots, about 20 minutes. Remove from grill; let cool 5 minutes. Finely chop charred broccoli florets. Stir together 3 cups broccoli, lemon juice, benne seeds, garlic oil, and 1 teaspoon salt in a medium bowl; set aside. (Reserve extra broccoli for another use.)
Bring cream to a boil in a large skillet over high. Reduce heat to medium, and simmer, whisking often, until cream is reduced and thickened enough to coat the back of a spoon, 6 to 8 minutes. Remove from heat, and stir in garlic. Add crab and remaining 1/2 teaspoon salt, and return to medium. Cook, stirring gently, until warmed through, about 2 minutes.
To serve, spoon crab mixture into 6 shallow bowls. Top evenly with broccoli mixture, and drizzle each with 1 teaspoon chive oil. Grate lemon zest over bowls. Garnish with lemon verbena and chopped chives. Cut zested lemon into wedges, and serve.
In lieu of grilling, broccoli may be oiled and roasted on a rimmed baking sheet at 500°F for 15 minutes.