Combine the asparagus, peas, and water in a saucepan over medium heat. Cover the saucepan and cook until the vegetables are beginning to become tender, yet retain some crispness, about 5 minutes; drain any remaining liquid and set the vegetables aside.
Melt the butter in the saucepan over medium-low heat. Stir the flour into the butter until combined, 2 to 3 minutes. Add the milk, raise heat to medium and cook, whisking frequently, until the mixture thickens, another 2 to 3 minutes. Stir the garlic powder and Parmesan cheese into the sauce; season with salt and pepper. Set aside.
Bring a pot of lightly salted water to a boil. Cook the fettuccine in the boiling water until the pasta is cooked yet firm to the bite, about 8 minutes; drain and return the fettuccine to the pot. Stir the vegetables, the sauce, and the prosciutto into the fettuccine.