I pretty much did the below, except that I didn't make the lemon mayonnaise. Short of that, it was pretty dang good, and the first time I've ever not dipped Artichoke in mayo. (lost 30 LBS, have 15 LBS to go) the video link below is worthy
ARTICHOKES:
4 large artichokes, rinsed well, top third removed, and leaf tips trimmed
1/4 cup salt, plus ½ teaspoon
2 lemons, halved
1 cup olive oil
1/3 cup balsamic vinegar
1 tablespoon chopped garlic
1 tablespoon chopped parsley leaves
1/4 teaspoon freshly ground black pepper
CHARRED LEMON MAYONNAISE:
2 lemons, halved
1 large egg (see Cook’s Note below)
2 to 3 tablespoons water
1/2 cup olive oil
1/2 cup vegetable oil
1/2 teaspoon salt
Pinch cayenne
Artichokes: Fill a large pot with water until its three-quarters full. Add 1/4 cup the salt and bring to a boil. Rub the cut sides and bottoms of the artichokes with the lemon wedges and carefully add them to the boiling water. Weight the artichokes as necessary with a heavy dish or bowl, and simmer, partially covered, until the bottoms are just tender and can be pierced with a sharp knife and an outer leaf pulls out easily, about 15 minutes. Drain the artichokes upside down in a colander until cool enough to handle.
Cut the artichokes into quarters and discard the prickly purple leaves and hairy choke.
In a bowl, combine the olive oil, vinegar, garlic, parsley, remaining ½ teaspoon salt, and pepper. Add the artichoke quarters and toss to coat. Let marinate for 2 to 4 hours, turning occasionally.
Preheat the grill to medium-high.
Remove artichokes from the marinade and grill, turning, until warmed through and lightly charred around the edges, about 5 minutes. Place on a platter and serve with mayonnaise on the side for dipping.
Mayonnaise: Preheat the grill to medium-high.
Place the lemon halves, cut sides down, on the grill and cook until charred, 5 to 10 minutes.
Squeeze lemon juice into the bowl of a blender or food processor. Add the egg and 1 tablespoon water and process for 20 seconds. With the processor running, slowly pour in the olive and vegetable oils through the feed tube and process until emulsified, adding additional water, 1 tablespoon at a time, to thin the mayonnaise to drizzling consistency. Add salt and cayenne and pulse to combine.
Adjust the seasoning to taste, transfer to an airtight container, and refrigerate for at least 30 minutes before using. Mayonnaise will keep refrigerated for up to 24 hours. Makes about 1 1/4 cups.