In a large bowl, beat the cream cheese, shredded cheese, chives, lemon zest and salt with a wooden spoon or spatula until well blended. Spoon onto a large piece of plastic wrap and form into an even 1-inch-diameter log. Refrigerate until firm, at least 2 hours or up to overnight.
In a small pot, combine the pomegranate juice, hot honey, sugar and cardamom. Bring to a boil over medium heat, then let the sauce cook and reduce until thickened, about 20 minutes. (It should coat the back of a spoon and have a glazelike consistency.) Keep warm or serve at room temp.
Unwrap the cheese log and place on a platter. Garnish the log with the pistachios, pomegranate seeds and a generous drizzle of the pomegranate syrup. Serve with your favorite crackers.