Cut or snap off the woody ends of the asparagus, then cut the stalks into 1 cm pieces.
Shell the peas and broad beans.
Sauté garlic, celery, and onions over low heat in the olive oil for about 10 minutes until the onions are translucent.
Divide asparagus, peas, broad beans, and green beans into two bowls.
Add one bowlful to the onion mixture, and let the vegetables sauté, stirring occasionally, for 5 minutes.
Season with sea salt and black pepper.
Pour in the chicken stock and bring the soup to a boil.
Let it simmer for 15 minutes.
Add the remaining vegetables and cook for an additional 10 minutes.
Remove the pot from the heat and stir in the basil and cream.
Let the soup cool to room temperature, then serve with Parmesan and pesto.