Step 1Heat the oven to 375 degrees.
Step 2To prepare the artichokes: Fill a bowl with cool water and add the juice of 1 lemon. Hold an artichoke in one hand with the stem facing toward you and the tip facing away. Slowly turn the artichoke against the sharp edge of a knife while making an abbreviated sawing motion. (It's easier to control if you use the base of the knife rather than the tip.) You will begin to cut through the tough outer leaves; when you can discern the natural cone shape of the artichoke, adjust the knife to follow it. Keep trimming until you've cut away enough of the tough leaves so you can see only light green at the bases. Cut away about the top half-inch of the artichoke tip and dip the artichoke into the lemon water so the cut surfaces don't get discolored.
Step 3With a paring knife, trim away the very tip of the stem, then peel the stem and base of the artichoke, going from the tip to where the base meets the leaves. You'll have to do this at least five or six times to make it all the way around the artichoke. When you're done, there should be no dark green tough spots left, only pale green and ivory.
Step 4Cut each artichoke into lengthwise quarters, and if there is a fuzzy choke inside, cut just below the choke to the very base of the leaves and the choke will pop off, leaving a clean heart below. Place the artichoke in the lemon water and go on to the next artichoke.
Step 5To prepare the fennel, trim away the dried-out bottom of the bulb. Cut the bulb in quarters lengthwise and slice away most of the triangular solid core at the center, leaving just enough to hold the bulb together. Cut each wedge in half again lengthwise to make 8 lengthwise wedges from each bulb.
Step 6Slice the potatoes in half lengthwise
Step 7Transfer all of the vegetables into a mixing bowl. Add the minced garlic, cracked pepper flakes, orange zest, the leaves of two to three sprigs of fresh thyme, the salt and olive oil and mix well with your hands to make sure the vegetables are all evenly covered with oil and flavorings.
Step 8Spread a rectangular sheet of parchment paper or aluminum foil on a work surface. You'll need a sheet at least 2 feet long and 1 foot wide. You can also bake this in 6 smaller individual-serving-size packets.
Step 9Arrange the oiled vegetables in a low mound centered on half of the paper and top with the olives. Fold the other half of the paper over and fold and crumple the edges together to form a tight seal. Place the packet on a jellyroll pan and bake until the potatoes are tender, about 45 minutes.
Step 10Remove from the oven. If you wish, serve the vegetables in their baking paper, cutting an "X" in the top at the table. Be careful, as there will be hot steam. Sprinkle lightly with coarse salt to taste and serve immediately.