This is a rustic, garlicky, potato-thickened soup with fresh artichokes and lemon. A wonderful supper soup for a chilly evening. You CAN substitute canned or frozen artichoke hearts for fresh. Not quite the same, but still yummy.
Fill large bowl with water and squeeze the lemon halves into it. Working with one artichoke at a time, trim the base, removing the stem and trimming the tough outer leaves beneath the heart. Cut off the top 2/3 of the leaves, leaving only the heart. With a small spoon, scrape out the hairy choke. Submerge the trimmed artichoke in the lemon water. Repeat with the five remaining artichokes. Once the hearts have been trimmed, slice them 1/4" thick and return them to the lemon water.
In a large deep saucepan, heat the 1/4 cup olive oil. Add the garlic and cook over low heat until softened but not browned, about 5 minutes.
Drain the artichokes and add them to the sauce pan along with the potatoes, the 6 1/2 cups of water and a pinch of salt. Bring to boil.
Put the peppercorns in a teaball or tie them up in a piece of cheesecloth and immerse them in the soup.
Simmer until both the peppercorns and potatoes are tender, about 30 minutes. Discard the peppercorns.
Using a fork or potato masher, partially mash the potatoes to thicken the broth. Season the soup with salt. Ladle into bowls and drizzle with olive oil. Serve with the lemon wedges.