For Dipping Sauce:
1. Whisk mayonnaise, Worcestershire sauce, canola oil, sesame oil, honey, lemon juice, ginger, and salt in small bowl, and mix well. Cover and refrigerate until cold.
1. Fill large bowl with cold water and add lemon juice. Cut off stem and top quarter of 1 artichoke. Bend back dark green outer leaves and snap off at artichoke base until only pale green and yellow leaves remain. Cut any dark green areas off base. Cut artichoke lengthwise into 6 wedges. Place artichoke wedges in lemon water. Repeat with remaining artichokes.
2. Steam artichokes until tender, about 30 minutes. Cool. Remove choke and any purple-tipped leaves from center of artichoke wedges.
3. Heat grill to medium-high heat. Stir olive oil and minced garlic in small bowl to blend. Brush garlic oil over artichokes. Sprinkle artichokes with salt and pepper. Grill artichokes until slightly charred, turning occasionally, about 8 minutes. Serve with dipping sauce.