Cook the jalapeno poppers according to package directions. Set aside to cool.
Position a rack in the upper third of the oven and preheat to 400 degrees F. Set a baking rack into a rimmed baking sheet.
Sprinkle the cutlets with salt and pepper. Put smooth side-down on a work surface with the short ends parallel to the edge of the countertop. Spread a fourth of the cream cheese over a cutlet, leaving about a 1/4-inch border. Lay a jalapeno popper across the short end closest to you and roll up to enclose the popper. Secure with a 6-inch wooden skewer. Sprinkle the cutlet with salt and pepper. Repeat with the remaining cutlets, cream cheese and poppers.
Put the flour in a shallow dish. Beat the egg until very loose in a second shallow dish. Put the breadcrumbs in a third shallow dish.
Coat the chicken roll-ups in the flour and the dip in the egg, letting any excess drip off. Then fully coat in the breadcrumbs. Transfer to a plate.
Heat the oil in a large nonstick skillet over medium-high heat. Place the roll-ups in the skillet, seam-side down, and cook until golden brown on all sides, turning as needed, about 5 minutes. Transfer the chicken to the rack on the prepared baking sheet. Bake until cooked through, about 15 minutes.
Remove the skewers from the chicken, cut each roll-up in half and serve.