Add the peas to a bowl and begin to mash them with the back of a fork until they are mostly broken down. Add the ricotta and use the fork to blend and mash them together. Add the Parmesan, lemon zest, chile flakes, garlic powder and onion powder and stir to combine. Set the mixture aside while you prepare the chicken.
Place the chicken cutlets between 2 pieces of parchment paper and pound them with a meat mallet or rolling pin until they are 1/4-inch thick. Remove the top layer of parchment paper and sprinkle the chicken with 1/4 teaspoon salt and 1/4 teaspoon pepper. Divide the pea and ricotta mixture evenly among the chicken cutlets, smoothing it out to cover the surface area.
Working one at a time, starting with the large end of the cutlet, roll the chicken up in a continuous spiral. Place the chicken on a plate seam-side down and continue the process with the remaining chicken.
Shingle 3 slices of prosciutto so they slightly overlap. Place one piece of chicken about a third of the way up from the bottom of the prosciutto. Similarly to wrapping a burrito, bring the base of the prosciutto up over the chicken, roll the chicken once, then fold in the ends of the prosciutto, so that the ends of the chicken are covered, and continue to roll until the chicken is completely wrapped in the prosciutto. Set aside and continue the process with the remaining chicken.
Heat a large ovenproof skillet over medium-high heat. Add the oil and swirl to coat the skillet. Add the prosciutto-wrapped chicken to the skillet and sear it on all sides. Transfer the skillet to the oven and cook until the chicken is cooked through and the prosciutto is golden and crisp, 15 to 20 minutes.
Remove the chicken from the oven and let sit for 5 minutes before serving.