Make the parsley dressing: put 3 tablespoons of the olive oil in a food processor along with the parsley, garlic, lemon juice and honey.Whizz until smooth and set aside.
Add the pasta to a large pan of boiling water and cook for 10-12 minutes until tender. Add the broccoli to the pan for the final 4 minutes of cooking time. Drain, then return the pasta and broccoli to the pan.
Meanwhile, heat the remaining 1 tablespoon of oil in a frying pan. Add the chicken and cook for 7 minutes, turning once, until golden brown and cooked through with no pink remaining.
Add the cooked chicken to the pan with the pasta and broccoli, then stir through the parsley dressing and the rocket. Scatter over the parmesan shavings, season with freshly ground black pepper and serve.