In a large pot of boiling salted water, cook the broccolini until crisp-tender, about 3 minutes. Drain, then run under cold water until cool; pat dry with a paper towel. In a large bowl, toss the broccolini with the EVOO; season with salt and pepper.
Heat a grill or a grill pan over high; cook the broccolini until tender and charred in spots, about 2 minutes per side. Transfer to a dish.
In a small bowl, whisk the tahini, lemon juice, honey and garlic. Whisk in 3 tbsp. water. Add more water by the tablespoonful, if needed, until the sauce is creamy and pourable. Season with salt. Drizzle over the broccolini and sprinkle with the sesame seeds.