Bring a large pot of salted water to a boil. Cook according to package instructions. Drain.
Meanwhile, in a large saucepan, heat cream with garlic cloves. Simmer for about 3 minutes. Whisk in butter to incorporate well. Add prosciutto and simmer for another 5 minutes until all ingredients are tender, warmed-through and well combined.
Add pasta to sauce pan and toss for 2 minutes on medium heat. Serve with pesto and grated Parmigiano-Reggiano.