Use a mandolin or a vegetable peeler to peel zucchini lengthways into ribbons. Thinly slice ribbons lengthways.
Heat the oil in a large saucepan over medium heat. Add the leek and garlic and cook, stirring, for 3 mins or until leek softens. Transfer to a bowl.
Add the stock, 2 cups (500ml) water and chicken to the pan. Bring to the boil. Reduce heat to low and simmer for 10 mins or until chicken is cooked. Transfer chicken to a chopping board and coarsely shred.
Add the pasta to the stock and cook for 5 mins. Add leek mixture, zucchini, asparagus and peas. Cook for 5 mins or until the vegetables are tender and the pasta is al dente. Stir in the chicken.
Meanwhile, to make the pesto, process basil, parsley, garlic, almonds, parmesan and lemon rind in a food processor until finely chopped. With the motor running, gradually add the oil in a thin, steady stream until combined.
Divide the soup among serving bowls. Top with dollops of pesto and sprinkle with lemon zest.