In a mixing bowl, whisk together the peanut butter, soy sauce, rice vinegar, brown sugar, chili garlic sauce, lime juice, pressed garlic, and grated ginger until smooth.
Whisk in 2 to 4 tablespoons warm water, a tablespoon at a time, until the sauce reaches a pourable consistency; adjust chili garlic sauce for desired heat.
Lay a tortilla flat and place about 1/2 cup baby spinach in the center, then add a portion of grated carrots, shredded cabbage, sliced red bell pepper, and about 1/2 cup cooked chicken.
Drizzle 2 to 4 tablespoons of the peanut sauce over the fillings, or use more if desired.
Fold the sides of the tortilla inward, then tightly roll from one end to make a wrap; repeat with remaining tortillas and ingredients.
Slice each wrap in half if desired and serve immediately.
