Heat the grill. Preheat grill to High heat (400-450 degrees F).
Make the dressing. Combine all ingredients for the lemon garlic dressing in a small bowl. Set aside.
Prep the broccolini. Remove excess leaves from the broccolini, and trim the bottom quarter inch of the stems. Lay the broccolini on a baking sheet and drizzle with the lemon garlic dressing.
Grill. Place the broccolini directly on the grill grates and grill for 8-10 minutes. Turn every 2-3 minutes. The stalks should have a bit of bend to them without being wilty and you should have some nice char on the edges.
Serve hot. Remove the broccolini from the grill and serve immediately.