Whisk together the peanut butter, hoisin sauce, and rice vinegar until smooth and pourable; warm 10 seconds in the microwave if it's too stiff to spread.
Toss the shredded chicken with 3 tablespoons of the peanut sauce until coated.
Spread the remaining peanut sauce over one tortilla, right to within 1/2 inch of the edge.
Layer half the sauced chicken, carrot, cabbage, and cilantro over the sauce.
Roll the tortilla tightly from the near edge into a firm log.
Wrap in plastic wrap and repeat with the second tortilla and remaining filling.
Refrigerate for at least 1 hour, until firm enough to slice without the vegetables sliding out.
Trim the ends and cut into 8 rounds with a serrated knife.
Arrange on a platter and serve chilled, with extra peanut sauce drizzled over the top if you like.
Good to Know
Shred the carrot and cabbage the night before and keep them in a paper-towel-lined container; they stay crisp and dry until you're ready to roll.