1. Combine the chicken stock, 2 tablespoons olive oil, peppercorns, salt, thyme, garlic, and shallots in a medium saucepan. Cut 2 lemons in half, and squeeze the juice through a small strainer directly into the saucepan. Set lemon halves aside.

2. Using a paring knife, trim about 1/2 inch from top of each artichoke. Remove and discard outside leaves so all that remains is tender lighter-green leaves. Use paring knife to trim stem end, and peel away tough outer skin. Slice artichokes in half. If center core is very purple, carefully carve out purple center, and discard. Rub each artichoke with lemon halves, and place in saucepan. Cover surface of cooking liquid with rinsed-out cheese-cloth to help keep artichokes submerged during cooking.

3. Set the pan over medium heat, and bring to a boil. Reduce heat, and allow to simmer until the artichokes are just fork tender, 35 to 40 minutes. Remove pan from heat, and allow artichokes to cool in cooking liquid.

4. Roast the red pepper on a grill or over a gas flame until charred on all sides. Place in a bowl, and cover with plastic wrap until cool enough to handle. Remove the skin by rubbing with a paper towel. Cut pepper in half, remove seeds and stem, and slice into long thin strips. Place the pepper strips in a bowl, and drizzle with olive oil.

5. Drain artichoke halves, discarding peppercorns and aromatics. Place in bowl. Squeeze juice of remaining lemon over artichokes, and drizzle with olive oil. Season with salt and pepper.

6. Using a knife, cut cheese into thin slices. Arrange cheese, peppers, and artichokes on serving plates. Place a quarter of the greens on each plate. Serve.