Begin, as usual with a soffritto: sauté the garlic gently in a generous amount of olive oil until it just begins to brown. Remove the garlic from the skillet and add your artichoke wedges. Increase the heat a bit and toss the artichokes in the seasoned oil for a few minutes without browning.
Add a splash of water (not a lot) and cover the skillet. Let the artichokes simmer until they are tender but not coming apart. Cooking time will vary according to the size, age and quality of your artichokes, and how thin your wedges are, but normally somewhere between 10-20 minutes will do.
Uncover the skillet, raise the heat, and season generously with salt and pepper, tossing the wedges to season them evenly. Then, at the last, add your parsley, give the skillet another toss, and serve immediately.