Cook the spaghetti in water with salt until al dente according to the instructions on the package. Heat 2 tbsp oil in the pan, and fry the chicken pieces for 4 minutes.
Chop the onion, crush the garlic, and cut the courgette into small cubes. Add all these to the chicken pieces, and fry for 8 minutes. Drain the spaghetti. Add the spaghetti and pesto to the chicken pieces and courgette. Season with salt and pepper.
Divide the spaghetti between the plates, and serve with the arugula topped with the cashew nuts.