Place the ground turkey, French onion soup mix, and black pepper in a large bowl.
Gently combine the ingredients without overmixing — overmixing creates a dense burger.
Divide the mixture into 6 equal portions and form each into a patty.
Press a shallow indentation into the center of each patty.
Heat olive oil in a large skillet over medium heat.
Add the turkey patties and cook for 5–6 minutes on the first side. Do not press down on the patties.
Turn the patties and continue cooking for 4–6 minutes, or until internal temperature reaches 165°F.
During the final minute, place a slice of Gruyère over each patty and cover the skillet until melted.
Remove from heat and allow to rest for 3 minutes
Serve on toasted brioche buns with garlic aioli, lettuce, and tomato — or in a lettuce wrap for a low-carb option.