Cook the pasta according to the package directions.
Heat the oil in a skillet over medium heat. Add the prosciutto and cook until crisp, about 2 minutes per side. Transfer to a paper towel-lined plate.
Add the garlic and shallot to the skillet and cook until softened, about 2 minutes.
Add the broth, peas, spinach, ¼ teaspoon salt, and ⅛ teaspoon pepper and bring to a boil. Toss with the pasta, Feta, basil, and prosciutto.