Place broth and cabbage in a large saucepan and set pan over medium-high heat. Bring to a simmer.
Arrange 16 wonton wrappers on a flat surface. Spoon filling onto the center of each wrapper, to within 1/4-inch of the edges (about 1 teaspoon per wrapper). Wet your fingers with water and pull up corners of the wontons to create individual "purses". Pinch the edges together (with wet fingers) to seal.
Place stuffed wontons in simmering broth. Cook 5 minutes, until wontons are tender and translucent. Remove from heat and stir in scallions.