Set a large pot of water on to boil over high heat. Build a charcoal fire, or preheat a gas grill. Line a baking sheet with parchment paper.

Remove the tough, dark outer leaves from the artichokes until the remaining leaves are half yellow, half light green. Cut away the woodiest part of the stem end and the top 1½ inches of every artichoke. If there are any purple inner leaves, cut them out, too. You may need to remove more in order to cut away everything fibrous. It might seem like you’re trimming a lot, but remove more than you think you should, because the last thing you want is to bite into a fibrous or bitter bite at the table. Use a sharp paring knife or a vegetable peeler to remove the tough outer peel on the stem and at the base of the heart, until you reach the pale yellow inner layers. As you clean them, place the artichokes in a bowl of water with the vinegar, which will help keep them from oxidizing, which makes them turn brown.

Cut the artichokes in half. Use a teaspoon to carefully scoop out the choke, or fuzzy center, then return the artichokes to the acidulated water.

Once the water has come to a boil, season it generously until it’s as salty as the sea. Place the artichokes in the water and reduce the heat so the water stays at a rapid simmer. Cook the artichokes until they are just tender when pierced with a sharp knife, about 5 minutes for baby artichokes and 14 minutes for large artichokes. Use a spider or strainer to carefully remove them from the water, and place them on the prepared baking sheet in a single layer.

Drizzle the artichokes lightly with olive oil and season with salt. Place the artichokes cut-side down on the grill over medium-high heat. Don’t move them until they begin to brown, then rotate the skewers until the cut side is evenly brown, about 3 to 4 minutes per side. Flip, browning the other side in the same way.

Remove from the grill and drizzle with a mint salsa verde, if desired, or serve with aïoli or honey-mustard vinaigrette. Serve hot, or at room temperature.