1. Fill a large bowl with ice water. Bring a pot of salted water to a boil. Add beans, and cook until just tender, about 5 minutes. Using a slotted spoon, plunge beans into ice water. Drain well. Keep water boiling, and refill bowl with ice water. Repeat with onions. Peel beans and onions.

2. Fill a large bowl with water and juice of 1/2 lemon. Remove tough outer leaves of artichokes. Trim tops and stems. Cut in half lengthwise, and transfer to lemon water to prevent discoloration.

3. Melt 2 tablespoons butter with the oil in a large saute pan over medium heat. Add shallot, and cook until soft, 2 to 3 minutes. Drain artichokes, and add to skillet along with onions, stock, wine, salt, and pepper. Bring to a simmer, and cover with a piece of parchment paper, then with a lid. Reduce heat to maintain a simmer, and cook until artichokes and onions are tender, about 20 minutes.

4. Add fava beans, and cook, uncovered, until tender and warmed through, about 2 minutes. Remove from heat. Swirl in remaining tablespoon butter until melted. Squeeze juice from remaining 1 1/2 lemons over the top. Season with salt and pepper, and serve.