Squeeze lemon juice from both lemons into bowl filled with the cold water. Trim artichokes of outer leaves and chop off the tough tip. Soak trimmed artichokes in lemon water after trimming each one to keep them from turning brown.

Place a large shallow skillet on med/hi heat. Add olive oil and garlic. Cook for one minute then add drained artichokes. Cook artichokes for about 3 to 5 minutes, stirring constantly. Add cayenne pepper, wine, 1/2 cup water, thyme, salt and pepper.

Cook on medium heat until liquid is reduced to about half. Serve with chopped parsley and grated Parmesan cheese on top.