Cook the pasta according to the package directions. Drain, reserving 1/2 cup of the cooking water.
Heat the oil in a large skillet over medium heat while the pasta cooks. Add the prosciutto and cook until crisp, about 2 minutes. Transfer to a paper towel-lined plate.
Return the skillet to medium heat. Add the shallot and cook until softened, about 3 minutes. Stir in the garlic and cook 1 minute. Stir in the peas, spinach, and 1/4 teaspoon pepper. Add the cooked pasta, Feta, and reserved pasta water. Cook, stirring, until the spinach wilts. Remove from heat and fold in the cooked prosciutto.
Divide among individual bowls and top with the basil.