Pulse together the cream cheese, lemon zest, garlic, 1/3 cup Parmesan, 1 teaspoon salt and a few grinds of black pepper in a food processor until smooth. Add the heavy cream and pulse until combined.
Arrange 1 box of artichokes around the perimeter of a 4-quart oval casserole dish with the stems pointing inward. Arrange any remaining artichokes in the box in the center of the dish. Spoon half of the cream cheese mixture over the artichokes making sure that the edges of the artichokes around the border are not covered. Repeat with the remaining box of artichokes and cream cheese mixture.
Mix together the panko, butter and remaining 1 tablespoon Parmesan in a small bowl. Sprinkle the breadcrumb mixture over the casserole making sure not to fully cover the exposed artichoke tips. Bake until the breadcrumbs are golden brown and the cheese sauce is bubbling around the edges, 25 to 30 minutes. Let sit for 10 minutes, then sprinkle with parsley and serve with lemon wedges on the side.
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