Fill a medium-sized bowl with cold water and squeeze the juice of the lemon into the water. Toss in the squeezed lemon rinds.
Trim the tops and the bottoms off the baby artichokes, pull off any tougher outer leaves, and cut them in half lengthwise. Toss them into the lemon water as you prep them (this will keep them from turning brown).
Heat the oil in a large skillet over medium heat. Sauté the leeks for 4 minutes, until they start to soften, seasoning them with salt and pepper.
Add the artichoke hearts, transferring them to the pan with a slotted spoon, and sauté for 1 minute, then add the broth and 1/2 cup of the lemon water, as well as the capers. Cover the pot, bring to a simmer over medium-high heat, then lower the heat to medium-low, and continue to simmer, covered, until the artichoke hearts are tender and can be pierced easily with a sharp knife, about 20 minutes. The liquid should be almost gone at this point; if there is still some left, uncover the pot and allow the artichokes to simmer for another few minutes until the liquid is almost evaporated. Taste and add salt and pepper as desired.
Transfer the braised artichokes to a serving dish and sprinkle with the parsley and the Parmesan, if using. Serve warm or at room temperature.
Notes
Make-Ahead and Storage
The trimmed, uncooked baby artichokes can stay in the lemon water in the fridge for up to a day.Leftover braised baby artichokes can be stored in the fridge for up to 5 days. Serve cold, room temperature, or gently reheat them in a pan on the stove or in the microwave.