Working with 1 artichoke at a time, cut off stem to the base. Remove bottom leaves and tough outer leaves, leaving tender heart and bottom; trim about 2 inches from the top of artichoke. Steam artichokes, covered, 20 minutes; cool to room temperature. Gently spread leaves; remove fuzzy thistle from bottom with a spoon.
Preheat oven to 375°.
Place potatoes in a saucepan; cover with water. Bring to a boil. Reduce heat. Simmer 12 minutes or until tender; drain. Beat at medium speed of a mixer or with a potato masher until coarsely mashed.
Heat oil in a nonstick skillet over medium-high heat. Add garlic; sauté 2 minutes or until golden. Remove from heat; add sherry, scraping skillet to loosen browned bits. Add sherry mixture, mozzarella, basil, salt, and pepper to potatoes.
Stuff about 1 cup potato mixture into each artichoke. Sprinkle with Parmesan. Place stuffed artichokes in an 8-inch square baking dish coated with cooking spray. Bake at 375° for 20 minutes or until artichokes are tender. Garnish with parsley, if desired.