Cook pasta in a large saucepan of lightly salted boiling water until al dente, following packet instructions.
For the pesto, combine spinach, basil, garlic and walnuts in a food processor. Process until finely chopped. With the machine running, add olive oil, lemon juice, salt and pepper. Process until smooth.
Drain pasta. Transfer to a large serving bowl. Add spinach pesto, capsicum and tomato. Toss gently to combine. Sprinkle with the parmesan.