1. Fill a large bowl with cold water; juice 2 lemons into water. Set aside. Trim spiky tops, tough stems, and outer leaves from artichokes; halve lengthwise. Scrape any pink choke out from the center, leaving artichoke half intact. Transfer cut artichokes to acidulated water immediately.

2. Drain artichokes. Fill a large saucepan with water. Add artichokes, garlic halves, peppercorns, 1 1/2 tablespoons salt, 2 tablespoons olive oil, and thyme to saucepan. Set over high heat; bring to a boil. Reduce heat; simmer, using a few layers of cheesecloth or a plate to keep artichokes submerged, until tender when pierced with a sharp knife, about 5 minutes.

3. Remove from heat, and drain. Reserve artichoke halves, some of the garlic, and a few sprigs of thyme. Place in a bowl, and drizzle with remaining 2 tablespoons olive oil. Season with remaining 1 1/2 teaspoons salt and pinch of pepper.