Heat the oven to 400F.
If your artichokes are large, cut them into quarters. If they are small, but in them in half. A big serrated knife will do the job best. Rub the slices of lemon on the cut surfaces of the artichokes to stop them going black. To make life easier, you can now scoop out the chokes with a teaspoon or the tip of a small knife.
If you have an oven-proof, shallow pan with a tight lid, place the artichokes in it, cut-side up and quite snug. If you don’t, just use a baking tray with sides. Place the lemon slices, thyme, and whole garlic cloves in between the artichokes. Pour the water and the wine on top, and sprinkle with the salt and peppercorns. Finally, drizzle with the olive oil. Cover with the lid, or with aluminum foil, if using a tray.
Place in a hot oven and bake for 30-40 minutes, until the leaves just come as you pull gently.
Remove the artichokes from the cooking liquid and serve warm.
Mix all of the dipping sauce ingredients together and serve with the warm artichokes.