Heat oil in a medium stock pot that all 4 artichokes can sit in and not able to roll over. Add onions and cook until translucent, then add garlic. Reduce heat to medium, to keep garlic from burning. Once garlic and onions are cooked, deglaze pot with white wine. Add the remaining ingredients and mix together.
Cut stems off artichokes, leaving 3/4-inch on bottom. If tops of artichoke have big thorns remove with scissors. Add artichokes to stock pot insuring that they do not roll over on their sides.
Fill stock pot with water with 2 inches of the artichoke out of the water. Boil the mixture, covered for approximately 20 minutes or until a center leaf is removable by tongs.
When done remove, let cool briefly and serve with mayonnaise or aioli of choice.
A viewer or guest of the show, who may not be a professional cook, provided this recipe. It has not been tested for home use.