Trim the tops and end of the stems with a knife, and snip the pointed tips off the leaves with kitchen shears.
Rub the artichoke with a lemon or squeeze the lemon into 1 cup of water and let the artichoke sit in the acidulated water while you prepare the remaining artichokes.
In a large pot with a steamer insert, bring a few inches of water to a boil.
Place the trimmed artichokes, cut top side down in the steamer.
Cover and steam for 25 minutes until artichokes are tender and leaves easily pull away. (35-45 minutes for large artichokes.)
Remove the artichokes carefully with tongs and allow to cool before handling. Artichokes and be covered and refrigerated up to a day before proceeding, if desired.
Preheat the grill to high.
Place the cut top side down on a cutting board and with a knife, slice through the center of the stem down to the board to create two halves.
With a spoon, carefully remove the fuzzy choke portion and discard. It should separate easily from the heart.
Drizzle the cut side of the artichoke halves with olive oil and sprinkle with lemon pepper or salt and pepper.
Grill artichokes 5-8 minutes, starting cut side down, turning once until warmed through and slightly charred.
Drizzle with olive oil, fill with the crispy stuffing, and serve with the creamy lemon dipping sauce.