Heat a wok over high heat, then add 2 tablespoons of oil. Stir-fry the garlic and sliced green onion whites for about 30 seconds until fragrant, then add the chicken and stir-fry until it is almost cooked through. Add the soy sauce, peanut butter, lime juice, shredded carrots, sugar, red pepper flakes, and sliced green onion greens. Stir-fry for 1 minute until well combined, then remove the wok from the heat and let the filling cool to room temperature (about 10 minutes).

Divide the cooled mixture between the wonton wrappers (about 1 heaped teaspoon per wrapper). Dip your fingertip in water and moisten the edges of each wrapper, then scrunch up the tops to seal, pressing firmly to remove any air pockets. Alternatively, divide the filling between 8 wrappers, moisten the edges, and press the remaining 8 wrappers on top to form ravioli shapes.

In the same wok (or a deep saucepan), heat about 2 inches (5cm) of vegetable oil to 370°F / 188°C. Working in batches of 4–5, carefully slide the wontons into the oil using a spider strainer. Deep-fry for 2–3 minutes, turning once, until evenly golden brown. Transfer to a paper towel-lined plate or wire rack to drain. Return the oil to 370°F / 188°C between batches.