In a bowl, mix together the Parmesan cheese and parsley. Set aside.
In a separate bowl, stir together the cream cheese, goat cheese, lemon zest, tarragon, and pepper until well blended and smooth. Gently fold in the artichoke hearts, being careful not to break pieces apart. Toss artichoke pieces into Parmesan and parsley until thoroughly coated.
Transfer artichoke pieces to a wax paper-lined baking sheet. Cover, and refrigerate for 1 hour, or until firm. Remove from refrigerator 30 minutes before serving. Serve slightly chilled.