When the artichokes have cooled, slice each artichoke in half, down the stem. Carefully handle the artichokes to avoid breaking off any leaves, since they're very tender after cooking.
Use a small spoon to scoop out and discard the fuzzy needle-like white centers and purple leaves from each artichoke half.
Arrange the artichokes on serving plates. Add toppings: lightly brush the cut surfaces with olive oil, and season with freshly ground black pepper, sea salt, and dried thyme leaves.
Serve them with the prepared dipping sauce and an empty discard plate for leaves.
To eat, peel off a leaf at a time (starting with the outermost leaves), dip into the sauce, and use your teeth to scrape off the meat of the leaf. Repeat until all of the leaves are gone. Only the heart and stem should remain (the best parts); the heart is completely edible, and the stem is edible if it's tender and not too woody.
Cover and refrigerate any leftovers. Reheat using the microwave.