Pulse ham, in batches, in a food processor 4 to 6 times or until shredded. (Do not overprocess.)
Stir together parsley and next 9 ingredients. Stir in ham until well blended. Cover and chill 8 hours. Store in an airtight container in refrigerator up to 3 days. Let stand at room temperature 30 minutes before serving. Serve with crackers and Quick Winter Pickled Veggies. Garnish, if desired.