Step 1Snap the stem off an artichoke by holding one on its side against a cutting board and pressing down on the stem with your other hand. The stem should come off with fibers clinging to it. Repeat with the remaining artichokes.
Step 2Put the artichokes in a wide pot large enough to hold them in a single layer. Add cold water to cover by 1 inch (about 4 quarts), then add the salt. Cover and bring the water to a boil over high heat.
Step 3Reduce the heat to medium and boil, covered, until a paring knife pierces through the base easily, 45 to 55 minutes.
Step 4Meanwhile, put the shallot in a medium bowl and sprinkle with a pinch of salt. Heat the oil in a small saucepan over medium heat until shimmering but not smoking, about 2 minutes. Immediately pour the hot oil over the shallot. Once the sizzling dies down, stir in the vinegar and a pinch of piment d’espelette.
Step 5Use a slotted spoon to transfer the artichokes to a colander set over a bowl to catch dripping hot water. Let stand until cool enough to handle, about 10 minutes.
Step 6Put the artichokes upright on serving dishes. Gently press down on the top of each with your palm to open the petals like a blooming flower. Stir the vinaigrette again and season to taste with salt and pepper. Spoon half the vinaigrette over the artichokes and transfer the remaining to serving dishes.
Step 7Serve warm, plucking off the petals and dipping the bottoms into the vinaigrette to eat the meat by scraping it off with your teeth. Discard the tops of the petals. When you get to the center, cut the artichoke hearts in half and cut out and discard the fuzzy chokes if you’d like. Dip the hearts in the vinaigrette and eat.