Bring a large pot of salted water to a boil. Cook the pasta until al dente. Drain, reserving 1/2 cup pasta cooking water.
Meanwhile, in a large nonstick skillet, heat 1 tablespoon olive oil over medium-high heat. Add the prosciutto and cook until browned, about 5 minutes; drain on paper towels. Add the remaining 3 tablespoons olive oil to the pan and increase the heat to high. Add the cantaloupe, season with salt and cook until a chunky sauce forms, about 7 minutes. Stir in the tomato paste and simmer for 1 minute; stir in the lemon juice and cream and remove from the heat.
Add the pasta, lemon peel, 1/4 cup parmesan cheese and half of the crispy prosciutto to the sauce. Toss to combine, adding some of the reserved pasta cooking water, if needed, to make a thinner sauce. Season with pepper, serve with the remaining prosciutto and sprinkle with more parmesan.