Cut away the tops of the asparagus (about 4-5 cm length).
Put the green peas to the boiling salted water and cook for 2 minutes; add the asparagus tops, cook for 1 minute, and finally add the asparagus stalks and cook everything for 30 seconds longer; immediately after that transfer the vegetables to a bowl with ice cold water; drain well.
Using a vegetable peeler strip ribbons of the asparagus stalks.
In a small bowl make the dressing by mixing the olive oil, lemon juice, and chopped basil.
Arrange on a big plate (or on separate plates) the green peas, asparagus tops, asparagus ribbons, halves of tomatoes and prosciutto, drizzle with the dressing and sprinkle with the Parmesan shavings.