Combine 2½ quarts of water, 2 tablespoons of salt, peppercorns and 2 of the bay leaves in a large pot and bring to a boil.

Trim the tough outer skins from the artichoke stems and remove the bottom row of leaves. Carefully add the artichokes and lemon halves to the boiling water and return to a boil. Using tongs, place a heavy heat-resistant plate on top of the artichokes to keep them submerged, reduce the heat and cook at a low simmer until the artichokes are tender and a paring knife inserted into the heart pierces easily, about 20 to 25 minutes. Drain in a colander and let sit until cool enough to handle.

Remove the large outer leaves and scrap the meat from each into a small bowl. Remove and discard the spiky inner leaves. Scrape the hairy choke from the hearts and discard. Roughly chop the hearts and the stems and add to the bowl of artichoke meat. Set aside.

Melt the butter in a Dutch oven over medium-high heat. Add the onions, celery and carrots and cook, stirring until soft, 2 to 3 minutes. Add the garlic, parsley, thyme and the remaining bay leaf and cook, stirring until the garlic is fragrant, 30 to 45 seconds.

Add the reserved artichoke meat, chopped artichoke hearts and stems and the flour and cook, stirring constantly until the flour is incorporated into the mixture. Add the remaining ingredients including the oysters and their liquor, stir well and bring to a boil. Reduce the heat to a medium-low and simmer uncovered stirring occasionally for 30 minutes. Remove the bay leaves and discard.

Remove the soup from the heat and using an immersion blender or in batches in a food processor, puree until smooth. Adjust the seasoning to taste.

Ladle the soup into bowls and serve immediately.