Heat 2 tablespoons of the oil in a large nonstick frying pan over medium heat.
Add the carrot, celery, onion, and sage, season with salt and pepper, and cook, stirring occasionally, until the onions and carrots have softened, about 10 minutes.
Transfer the mixture to a plate to cool and wipe the pan clean with a dry, clean towel or paper towels; set the pan aside.
Grind the turkey, potatoes, and cooled vegetables through a hand crank meat grinder into a bowl.
Add the remaining measured ingredients to the bowl (except for the oil) and stir to combine.
Using your hands, form the mixture into 6 patties (4 inches wide, about 2/3 cup each) and place on a baking sheet.
Heat the remaining 2 tablespoons of oil in the reserved frying pan over medium heat until shimmering.
Add 3 of the patties and cook undisturbed until the bottoms are dark golden brown, about 8 minutes.
Using a flat spatula, carefully flip the patties over and cook until they're dark golden brown on the other side, about 8 minutes more.
Transfer to a large plate and repeat with the remaining patties.