Add the remaining 3 tablespoons olive oil, the onions, cumin, garlic, tomatillos and water to the pan and bring to a boil. Return the chicken pieces to the pan, return to a boil, reduce the heat to maintain a simmer, and cook for 20 minutes, until cooked through.

Remove from the heat and allow to cool. Remove the chicken, shred it, and set aside.

Puree the tomatillo mixture in a blender and pour it into a bowl. Add the shredded chicken to the sauce mixture and add the jalapenos, cilantro, lime zest, lime juice and scallions, and stir to mix well. Season with salt and allow the filling cool.

Warm the tortillas in the microwave for 1 minute. Working with one warm tortilla at a time, spread about 2 full tablespoons of the filling across the center of each tortilla. Roll up the tortilla and close each at the seam with a wooden toothpick. Keep the rolled tortillas covered with a moist towel. The flautas may be prepared to this point up to 4 hours in advance.

Make the pico de gallo: Place the tomatoes in a bowl with the pickled jalapenos and the serranos, then add the lemon zest, lemon juice and cilantro and stir. Set aside.

Assemble the dish: In a large skillet, heat 1 inch of vegetable oil over moderately high heat until it registers 360 F on a deep-fry thermometer. Fry the flautas in batches, seam side down, turning them, for 1 to 2 minutes, or until they are crisp. As they are finished, use tongs to transfer them to paper towels to drain. Season with salt while still very hot.

Season the pico de gallo with salt and pepper. Serve the flautas with the pico de gallo.

(Mario Batali is the award-winning chef behind twenty-five restaurants including Eataly, Del Posto, and his flagship Greenwich Village enoteca, Babbo.)