Preheat An Outdoor Grill For Medium-High Heat, And Lightly Oil The Grate. Stir The Cranberry Sauce, Horseradish, Lemon Juice, And Cumin Together In A Bowl. Season To Taste With Salt And Pepper, And Set Aside. Mix The Egg, Celery, And Onion In A Bowl With Your Hand Until The Egg Is Smooth. Add The Turkey, Thyme, Poultry Seasoning, Parsley, And Bread Crumbs; Mix Until Evenly Combined. Form The Turkey Mixture Into 8 Patties. Cook The Turkey Burgers On The Preheated Grill Until No Longer Pink In The Center And The Juices Run Clear, About 4 Minutes Per Side. An Instant-Read Thermometer Inserted Into The Center Should Read At Least 165 Degrees F (74 Degrees C). Place Onto The Hamburger Buns, And Top With Cranberry Sauce To Serve.