To make the lemon parsley butter, melt the butter and mix with the lemon juice and chopped parsley. Allow to cool slightly, then taste and season as necessary.
Prepare the Artichokes
Fill a large pot with an inch of water and add a steamer to the pot.
Use scissors to cut any pointy edges on the artichoke leaves.
Use a vegetable peeler to remove the outer layer of the artichoke stems. Cut off the top 1/2 inch of the artichokes.
Slice the artichokes in half and scoop out the fuzzy part called the choke and inner leaves.
Heat the pot of water on high heat until it reaches a boil. Then reduce the heat to medium-high and place the artichoke halves in the steamer.
Cover the pot and steam for 20 minutes or until you can easily pull off the outer leaves, and you can pierce the heart effortlessly with a knife.
Grilling the Vegetables
Preheat the grill to medium heat, 350°F to 450°F.
Place the vegetables in a grilling pan and grill for 5-10 minutes, turning once until desired tenderness.
Toss the grilled vegetables with the parsley butter while still warm. Serve immediately.