If you’re using bamboo or wooden skewers, soak them in water for 30 minutes. Meanwhile, start the coals or heat a gas grill for hot direct cooking. Make sure the grates are clean.
Bring a large pot of salted water to a boil. Trim the brussels sprouts and remove any discolored outer leaves. Add the sprouts and blanch until just soft enough to pierce with a skewer, 8 to 12 minutes. Drain, then pat dry with paper towels. Toss with 1 tablespoon of the oil in a bowl. When cool enough to handle, thread 4 to 6 sprouts on each skewer.
Make the dipping sauce: Put the parsley, lime juice, garlic, and remaining 2 tablespoons oil in a blender or food processor and process until chopped, stopping to scrape down the side of the container if necessary. Add the olives and pulse until the mixture is a rough puree. Taste and add a little salt if you’d like. Transfer to a small serving bowl.
Put the skewers on the grill directly over the fire. Close the lid and cook, turning once or more, until the brussels sprouts are tender all the way through and browned, 3 to 5 minutes per side. Transfer to a serving plate and serve with the dipping sauce on the side.
Adapted from How to Grill Everything, © 2018 by Mark Bittman. Reproduced by permission of Houghton Mifflin Harcourt.