Step 1Fill a large bowl halfway with cold water. Halve the lemon, squeeze its juice into the water, then add the spent rinds to the water.
Step 2With a folded kitchen towel in one hand to protect your fingers, use a paring knife to trim off any tiny spines and leaves from the undersides of one cardoon stalk. Use the knife to pare off the strings from the top side of the stalk, like you would for celery. Flip the stalk over and, with the tip of your knife, scrape off any tiny rough skin from the bottom, too. Finally, cut the stalk on a diagonal into rough 1 1/2- to 2-inch-long pieces, discarding the dark ends, and immediately place them in the lemon water to keep them from browning. (Go online to latimes.com/Food, for a link to a video.) Repeat with the remaining cardoon stalks; you should have 4 to 5 cups, depending on size.
Step 3Bring a large pot of salted water to a boil. Drain the cardoon pieces and transfer them to the boiling water. Boil the cardoon pieces for 5 minutes, then drain them again and refill the pot with water to cover the cardoons. Bring the water back to a boil and cook the cardoon pieces until the tip of a paring knife pierces each piece with very little resistance and the pieces are tender when you bite into them, about 1 hour more. Add more water as needed to keep covered.
Step 4While the cardoons boil, make the vinaigrette: Using a vegetable peeler, pare off the orange’s zest in wide strips, avoiding as much of the white pith as possible. Working in batches, stack the zest strips on top of one another, and use your knife to slice them lengthwise into super-thin matchsticks (or as thin as you can get them). Juice the orange into a bowl (you should get about 1/3 to 1/2 cup juice) and whisk in the olive oil, followed by the orange zest strips, olives and thyme.
Step 5When the cardoons are tender, drain them, then transfer them to the bowl with the vinaigrette and toss to combine. Allow the cardoons to cool to room temperature, tossing occasionally in the vinaigrette to make sure they’re soaking it all up evenly, and season with salt. Transfer the bowl to the refrigerator and let the cardoons chill, at least overnight or up to three days. Season with black pepper before serving.