1. Fill a large bowl with cold water. Cut the lemons in half, squeeze the juice into the bowl, and toss in all but one of the halves. Keep that last half nearby. 
2. Trim the artichoke stems to about an inch from the base so they’ll sit flat in the pan. If the stems are thick, use a paring knife to peel away the tough outer layer. Remove the tough outer leaves until you reach the softer, paler ones. Cut about an inch off the top to remove the sharp tips, then snip off any remaining prickly points with scissors. Rub all cut surfaces with the reserved lemon half and drop each artichoke into the lemon water as you go.
3. When ready to cook, remove the artichokes from the water. In a heavy-bottomed pot or Dutch oven large enough to hold all four artichokes, warm 2 tablespoons of olive oil over medium heat. Add the garlic and cook until fragrant, about 30 seconds.
4. Pour in the wine, add the bay leaf, lemon zest and juice, and bring to a boil. Let the wine cook uncovered for 1–2 minutes to allow the alcohol to begin evaporating. Reduce to a gentle simmer. (Hold off on seasoning the liquid until it has reduced, or it can turn too salty.)
5. Nestle the artichokes stem-side down in the pot. Cover partially, leaving the lid slightly ajar, and simmer gently until the artichokes and stems are completely tender, 20 to 30 minutes depending on size. You’ll know they’re ready when a leaf slips away with almost no effort and a knife meets no resistance at the base. (When checking the pot, lift the lid slightly away from you first to allow the steam to escape before fully opening.)
6. Once tender, remove the artichokes and set aside to cool slightly, reserving the poaching liquid. Once cool enough to handle, cut each artichoke in half lengthwise and use a spoon to scoop out and discard the fuzzy choke.
7. Meanwhile, bring the poaching liquid to a boil and cook until reduced by half, about 10 minutes. Season to taste with salt.
8. Warm the remaining 2 tablespoons of olive oil in a large sauté pan over medium heat. Place the artichokes cut-side down and cook until nicely golden, about 5 minutes.
9. Transfer to a platter. Drizzle with the reduced poaching liquid and your best extra-virgin olive oil. Scatter with chopped parsley, a pinch of sea salt, a handful of toasted pignoli, and finish with generous shavings of Pecorino Toscano. Serve warm or at room temperature.

To eat: pull the leaves one by one and scrape the tender base of each leaf with your teeth. When you reach the heart, the whole thing is edible. Don’t leave a drop of that sauce on the platter.