Cook the pasta according to packet instructions. Meanwhile, toast the walnuts in a dry pan for a few minutes.
To make the pesto, add half the walnuts to the small bowl of a food processor or a hand chopper, along with the red peppers, Parmesan, garlic, basil, olive oil and some seasoning. Whizz to a paste, adding a splash of water from the pasta if it is a little dry.
Drain the pasta, reserving a cup of the cooking water. Return the pasta to the pan and set over a low heat. Add the pesto from the food processor, the mascarpone and 3 to 4 tablespoons of the reserved pasta water, then stir until the mascarpone has melted, adding a splash more pasta water if the sauce needs thinning.
To serve, crush the remaining walnuts in your hand and scatter over the pasta with a few more basil leaves and some extra Parmesan cheese.