Trim the top 1-inch off of the artichokes and peel the outer leaves off to the tender light green ones. Quarter each artichoke into wedges. If not cooking immediately, place in lemon water to prevent browning. Cut potatoes into four wedges.
In a large skillet, on medium-high heat, saute the potatoes and artichokes in oil and butter for 5 minutes so the potatoes just start to brown. Add garlic and saute until garlic just starts to brown. Add chicken stock. Turn down heat and continue cooking for 15 minutes. Chicken stock should reduce down to a 1/2 cup. Season with salt, pepper, and parsley.