In a skillet over medium heat, heat the olive oil or butter. Add diced onion and celery. Cook for 5–7 minutes until soft and translucent. Set aside to cool slightly.
In a large bowl, combine chopped turkey, breadcrumbs, cranberries, parsley, thyme, salt, and pepper. Mix thoroughly.
Add the sautéed vegetables, beaten egg, and ⅓ cup of chicken broth. Mix well. If the mixture feels dry or crumbly, add broth 1 tablespoon at a time until it holds together when pressed.
Refrigerate the mixture for 20–30 minutes to firm up and make shaping easier.
Scoop about 2 tablespoons of the mixture and roll into balls. Place on a parchment-lined baking sheet or oiled air fryer tray.
Preheat oven to 375°F (190°C). Bake for 22–25 minutes, until golden brown and firm to the touch.
Preheat air fryer to 360°F (182°C). Cook for 12–15 minutes, shaking halfway through, until crisp on the outside.
Serve warm with gravy, cranberry sauce, or as part of a holiday plate.