Remove the tough inner core from the cabbage and discard. Mince the leaves. You should have about 1 1/4 cups of cabbage when done.
Add the cabbage, meat, scallions, carrots, garlic, salt and pepper to a deep bowl. Stir with a fork to mix well.
Lay 6 wonton wrappers on a counter or cutting board. Fill a small bowl with cold water, and keep it nearby. Spoon 1/2 teaspoon of the filling into the center of each wrapper. Using your finger, dab the edges of the wrappers with a bit of water. Fold the wrappers in half to form a triangle, and press the edges to seal them closed. Fold the tips of the longer edges together, tucking one underneath. Lay the formed wontons flat on a parchment-lined baking sheet. Repeat with the remaining filling and wrappers.
Fill a skillet with 1 inch of oil. Heat over medium heat until shimmering. Add the wontons in batches, being careful not to crowd the pan. Fry until deep golden on the bottom, 2 to 3 minutes. Turn, and cook until golden on the other side, 2 to 3 minutes more. Transfer to a paper towel-lined plate to drain. Serve hot.
This recipe was originally made using beef burgers, but you can substitute turkey or chicken burgers to make the wontons.