Make the crispy prosciutto: Preheat the oven to 400°F and arrange the prosciutto in a single layer on a parchment-lined baking sheet. Bake for 8–10 minutes until crisp, then let cool before breaking into small pieces.
Make the chili crisp breadcrumbs: Toast the sourdough until golden and crisp, then let it cool slightly. Add it to a food processor and pulse into coarse breadcrumbs. Toss the breadcrumbs with the Calabrian chili crisp until evenly coated and set aside.
Make the Caesar dressing: Whisk together the mayonnaise, anchovies, garlic, lemon juice, Dijon, Worcestershire, Parmesan, and Calabrian chili crisp. Season with black pepper and thin with a splash of water as needed until creamy but pourable.
Prep the chicken: Pound the chicken cutlets to about ¼-inch thick. Set up three shallow bowls: one with flour, one with the eggs whisked with milk, and one with the panko, Parmesan, garlic powder, salt, and pepper.
Bread the cutlets: Coat each chicken cutlet first in flour, shaking off the excess, then dip into the egg mixture and finally press firmly into the seasoned panko mixture until completely coated.
Fry the chicken: Add about ¼ inch of neutral oil to a large skillet and heat over medium-high heat. Fry the cutlets for about 3–4 minutes per side, or until deeply golden, crisp, and the thickest part reaches 165°F. Transfer to a wire rack or paper towel-lined plate and season with flaky salt.
Dress the salad: Add the romaine to a large bowl with the Parmesan and enough chili crisp Caesar dressing to thoroughly coat the leaves. Toss until evenly combined.
Assemble: Divide the Caesar salad between plates and top each with a crispy chicken cutlet. Sprinkle generously with the Calabrian chili crisp sourdough breadcrumbs and crispy prosciutto. Add extra Parmesan, cracked black pepper, and a squeeze of fresh lemon before serving.