Cook Pasta: Cook the spaghetti in well-salted boiling water until it is al dente. Before draining, reserve 1/4 cup of the starchy cooking water.
Crisp Prosciutto: In a large sauté pan, heat a small amount of olive oil. Add the diced prosciutto and cook until it is crispy. Remove the crispy prosciutto and set it aside, leaving the rendered fat in the pan.
Sauté Aromatics: Add a knob of butter to the pan. Once melted, add the minced garlic and Calabrian chilis. Gently swirl the pan and cook until the mixture is fragrant (do not brown the garlic).
Deglaze and Simmer Sauce: Pour in the white wine and bring it to a boil, swirling the pan to deglaze. Next, add the reserved clam juice and the 1/4 cup of reserved pasta water. Reduce the heat and simmer the sauce for approximately 10 minutes, allowing it to thicken slightly.
Finish Pasta: Transfer the al dente spaghetti directly into the simmering sauce. Continue cooking and tossing the pasta in the pan until it is fully cooked and the sauce has reduced and coats the pasta.
Assemble Dish: Remove the pan from the heat. Fold in the drained clams, grated Parmesan, and the crispy prosciutto. Swirl the pan until the sauce emulsifies, thickens, and thoroughly coats the spaghetti. Serve immediately.