Fill a large stock pot with 4 inches of water and bring to a boil.
Using a sharp knife, cut off 1/2 an inch off the top of the artichoke. Trim the artichokes using kitchen shears and peel the stem with a vegetable peeler until the stem is white. Cut the artichokes in half. Using a spoon, scoop out the choke.
Add kosher salt to the pot to season the water and place the artichokes in the pot cut side down. Turn the heat to a simmer and cook until the heart is tender when poked with a knife, approximately 30 minutes.
Using tongs, transfer to the artichokes to a plate lined with paper towels and allow to drain.
Brush the entire surface lightly with olive oil and place directly on the grill rack over med-high heat. Grill the artichokes for 2-3 minutes on each side or until lightly charred. Transfer to a platter and keep warm.
In a food processor, add the garlic, mayonnaise, yogurt, cheese, vinegar and mustard. Process until smooth. Season with salt and pepper to taste.
Serve with the artichokes and lemon wedges, if desired.
Notes
Don’t toss leftovers – The dipping sauce is stellar on burgers, grilled veggies, or as a veggie dip.
Stash for later – Boiled artichokes can be refrigerated for up to 3 days; sauce keeps up to 5 days.
Char char baby – Adjust char time for extra smokiness or tenderness.
Serve hot or room temp – Perfect for party platters where oven space is tight.