Begin by preheating the broiler. Lightly season the pork chops with kosher salt. Heat 2 tablespoons of the olive oil in a large ovenproof skillet over medium-high heat. Working in batches to avoid overcrowding, coat the pork chops in the all-purpose flour, shaking off any excess. Place the dredged chops in the skillet and sear until golden on both sides, approximately 1 minute per side. Remove the cooked pork and set aside on a plate, reserving the unused flour for later.

Lower the heat to medium and add the minced shallot to the skillet. Cook, stirring frequently, until softened, about 3 minutes. Increase the heat to medium-high and incorporate the sage leaves along with 2 teaspoons of the reserved flour. Stir until the mixture becomes aromatic and starts to sizzle, around 30 seconds. Deglaze the skillet by adding the white wine and bringing it to a boil. Reduce the wine by half, which should take about 2 minutes. Pour in 1 cup of the chicken broth and return to a boil, cooking until the sauce slightly thickens, approximately 2 minutes. Return the pork to the skillet, spooning the sauce over the meat. Place one slice of prosciutto atop each pork chop, followed by a sprinkling of the fontina and Parmesan cheeses. Broil for 1 to 2 minutes, or until the cheese is melted and bubbling.

In a separate small saucepan, heat the remaining tablespoon of olive oil over medium heat. Add the chopped prosciutto and sauté until crisp, about 1 to 2 minutes. Stir in the peas, the remaining ¼ cup of chicken broth, and ¼ teaspoon of salt. Cover the saucepan and cook until the peas are tender, roughly 5 minutes. Uncover and increase the heat to medium-high, allowing the liquid to reduce, which should take about 1 minute. Serve the peas alongside the prepared pork, drizzling the sauce generously over the dish.