Bring a large pot of salted water to a boil. Add spaghetti and cook until al dente, about 8-10 minutes.
While the pasta cooks, heat olive oil in a skillet over medium heat. Add the prosciutto and cook until crispy, about 3-4 minutes. Remove prosciutto and set aside on a paper towel.
In the same skillet, add minced garlic and sauté for about 30 seconds until fragrant.
Pour in the heavy cream and add frozen peas. Cook for 4-5 minutes until the sauce slightly thickens.
Crumble the crispy prosciutto and add half back into the skillet, saving some for garnish.
Drain the pasta and add it to the skillet, tossing to coat with the cream sauce.
Serve the pasta in bowls, topped with remaining crispy prosciutto and freshly grated Parmesan cheese.