Remove 10 to 12 thin curls of zest from whole lemon with a 5-holed zester; cut lemon in half. (Or, use a potato peeler to remove 2 wide strips, then slice them into very thin strips.) Fill a large pot halfway with water and squeeze juice from lemon into pot; toss in squeezed halves.
Trim 3/4 in. off each artichoke stem and discard. Remove tough outer layer of remaining stem with a vegetable peeler. Cut 1 in. off tip of each artichoke and pull off cracked or especially thick leaves; discard. Snip spiky tips off remaining leaves.
Slice 1 artichoke in half lengthwise through the stem. Use your thumb and a serrated grapefruit spoon to grasp any red-tinged center leaves; pull to remove. Scrape out and discard choke. Slice in half again and place both quarters in pot with lemon-water. Repeat with remaining artichoke half and second artichoke.
Cover pot and bring to a boil over high heat. Remove lid and continue boiling until stems are tender and leaves pull off with little resistance, 15 to 20 minutes. Drain on paper towels and let cool.
Meanwhile, combine garlic, mayonnaise, thyme, and juice of remaining lemon half in food processor. Process 30 seconds, or until smooth. Season with salt and a pinch of black pepper. Garnish with reserved lemon zest. Serve artichoke quarters with dipping sauce.
Note: Nutritional analysis is per serving.