Heat 1 tsp (5 mL) vegetable oil in a large nonstick skillet set over medium-high heat. Crumble in turkey and brown well. Add the carrot, cabbage, green onions, ginger, soy sauce, salt and pepper. Cook, stirring for 3 to 4 minutes or until the cabbage is wilted. Remove from heat; cool to room temperature. Moisten two edges of each wonton wrapper with a little water. Place a rounded spoonful of the filling in the centre of each; fold to enclose, pressing to seal. Place on a baking sheet dusted with cornstarch to keep wontons from sticking. Cover with a damp towel.
Heat 1 tsp (5 mL) vegetable oil in a large nonstick skillet set over medium heat. Add a single layer of the wontons. Cook, without turning, for 2 minutes or until just golden on the bottom. Add 1/2 cup (125 mL) of water to the skillet. Cover and steam for 6 minutes or until all the water is evaporated and dumplings are tender throughout. Repeat with remaining dumplings, adding more oil to the pan as needed.
Sauce: Meanwhile, whisk the cranberry sauce with the soy sauce in a small saucepan; set over medium heat. Cook, stirring often until the sauce comes to a boil and is smooth and glossy. Cool slightly; stir in the ginger and green onions.
Makes 32 wontons.