Cook the fusilli in a large saucepan of boiling water according to the packet instructions, until al dente, adding the asparagus and broad beans for the last 2 minutes of cooking. Drain the pasta and vegetables, then return them to the pan.
Meanwhile, half-fill a deep frying pan with water and bring to a simmer. Add the salmon and return to a simmer. Cover and gently poach for 10 minutes, until the salmon is just cooking through. Use a slotted spoon to transfer it to a plate. Allow the salmon to cool slightly, then use a fork to break it into large flakes.
Stir the lemon zest, lemon juice, olive oil through the pasta and vegetables. Toss to combine. Add the salmon and parsley, season with freshly ground black pepper and toss to combine.
If you are using fresh broad beans, you’ll need about 1 lb broad bean pods. You can also use frozen broad beans – thaw them before using.
To peel broad beans, make a small slit at one end with your thumbnail and slip the bean from the skin. Smaller beans may not need to be peeled.