Prepare a grill for medium-high heat and lightly oil grate. Drizzle cauliflower florets and scallions with 4 Tbsp. oil; season with salt and pepper. Grill scallions, turning occasionally, until charred in spots, about 2 minutes. Grill cauliflower in a grill basket until tender and charred in spots, 8-10 minutes.
Blend ginger, garlic, cilantro, lime juice, and remaining 2 Tbsp. oil in a food processor, thinning with water if needed, until sauce is the consistency of yogurt; season with salt.
Chop scallions into 1-2 inch pieces, and then arrange cauliflower and scallions on a platter. Sprinkle with red pepper powder and sesame seeds and drizzle with sesame oil. Serve with cilantro sauce alongside.