Preheat an outdoor grill for medium heat and lightly oil the grate.

Melt butter in a skillet over medium-low heat. Add onion and celery; cook and stir until onion is soft and translucent, about 5 minutes. Transfer to a large bowl.

Add ground turkey, stuffing mix, and eggs to the bowl and mix until thoroughly combined with the vegetables. Form mixture into 16 evenly sized patties; unlike hamburgers, these patties will not change shape as they cook.

Grill on the preheated grill until no longer pink in the center and the juices run clear, about 5 minutes per side. An instant-read thermometer inserted into the center should read at least 165 degrees F (74 degrees C).

Place each patty onto a hamburger bun, then top with cranberry sauce and a dollop of whipped cream cheese to serve.