Stir together first 7 ingredients. Spoon 1 teaspoon mixture in center of each wonton wrapper. Moisten wonton edges with water. Bring corners together, pressing to seal.
Pour oil to a depth of 3 inches into a Dutch oven; heat to 375°. Fry wontons in batches until golden, turning once. Drain on wire racks over paper towels. Serve immediately with Peanut Dipping Sauce.