Prep the cabbage leaves: Gently remove 8–10 large outer cabbage leaves. Rinse and pat dry.
Trim the thickest part of the stem on each leaf so they bend easily without tearing.
Soften the leaves: Bring a large pot of salted water to a boil. Blanch the leaves for 45–60 seconds until bright green and pliable. Transfer to a towel-lined tray to dry.
Alternatively, microwave 2–3 leaves at a time for 30–45 seconds.
Mix the patties: In a bowl, combine ground meat, onion, garlic, egg (if using), salt, pepper, smoked paprika, onion powder, and oregano. Mix gently until just combined—don’t overwork it.
Form and season: Shape into 4–6 patties, slightly wider than you want them to finish, as they shrink when cooked. Press a small dimple in the center to prevent doming.
Cook the patties: Heat oil in a large skillet over medium-high.
Sear burgers 3–4 minutes per side for beef (longer for turkey), until browned and cooked to your preferred doneness. Add cheese in the final minute to melt.
Set up your wraps: Lay 2 cabbage leaves per burger, overlapping to cover any gaps. Place a patty in the center and add toppings and condiments.
Wrap and tuck: Fold the sides of the leaves over the patty, then roll from the bottom up like a burrito.
If needed, use a toothpick to secure.
Optional warm finish: For a melty, cozy finish, return the wrapped burgers to the skillet for 30–60 seconds per side over low heat, just to warm through.
Serve: Slice in half if you like and serve with a simple side salad or roasted veggies.