1. Preheat broiler on HIGH. Meanwhile cut potatoes in quarters. Place potatoes, water and salt in microwave dish; cook on HIGH 6-8 minutes or until tender. Drain and set aside.
2. For artichoke topping, chop artichokes and parsley; place into mixing bowl. Grate parmesan cheese and add all but 2 Tablespoons into bowl. Add mayonnaise and thoroughly stir artichoke mixture.
3. Flatten chicken to 1/2" thickness. Sprinkle both sides of chicken with rosemary, (salt and pepper to taste).
4. Add 1 tsp of oil to skillet (don't use nonstick cookware) and heat until shimmering. Add remaining 1 tsp of oil and 1 tsp rosemary with some salt & pepper to the potatoes; stir to coat.
5. Place chicken & potatoes, cut side down, into skillet. Cook 3-4 minutes or until chicken is golden brown. Turn chicken & potatoes over; cook an additional 3-4 minutes or until chicken is golden brown and centers are no longer pink.
6. Remove potatoes from skillet; set aside and keep warm. To finish chicken, spread artichoke topping evenly over chicken; sprinkle with reserved cheese. Place skillet on top rack setting and broil 4-6 minutes or until topping is deep golden brown.