Whisk mayonnaise, Sriracha, and lime juice until smooth. Chill the dipping sauce.
Stir cornstarch and water together to make a smooth slurry. Set aside.
Heat neutral oil in a large skillet over medium-high. Sauté garlic and ginger until fragrant.
Add ground chicken. Cook, breaking it up, until no longer pink.
Stir in cabbage, carrot, and scallions. Cook until just wilted and crisp-tender.
Season with soy sauce, rice vinegar, Sriracha, sesame oil, sugar, salt, and pepper. Toss well.
Pour in most of the slurry and cook until the juices thicken. Cool the filling completely.
Place a wrapper on a board. Add about 2 tablespoons filling near one corner.
Fold sides over the filling and roll tightly. Brush the tip with a little slurry to seal. Repeat.
Heat frying oil to about 350°F in a deep pot. Fry rolls in batches until golden, 3–4 minutes.
Drain on a rack and rest 3 minutes. Serve hot with the Sriracha-lime mayo.