Peel and grate 1-inch piece ginger. Halve, seed, and roughly chop serrano chile pepper. Roughly chop 1/2 small onion. Grate carrots. Finely chop cilantro. Shred 2 cups worth of rotisserie chicken, skin removed.
Mix the yogurt, 2 teaspoons lime juice, cilantro and a pinch of salt in a bowl. Cover and chill until ready to use.
Combine the ginger, serrano pepper, onion, cumin and 1/4 teaspoon salt in a mini food processor and pulse to make a thick paste. (Or finely chop and mash with the flat side of a knife.)
Heat the oil in a large skillet over medium-high heat. Add the ginger-chile paste and cook, stirring, until most of the liquid has evaporated and the mixture is slightly toasted, about 5 minutes.
Stir in the chicken, carrots, 1/4 teaspoon salt and 1/2 cup water and continue to cook, stirring, until the sauce is thick and the chicken is heated through, about 2 more minutes.
Spoon one-quarter of the chicken filling down the middle of each pita. Drizzle with some of the yogurt sauce and fold up.
Steam the green peas. Serve on the side. (Serving size: 1 wrap, 1/2 cup filling, 1/2 cup peas)