Cook the pasta in lightly salted boiling water according to package directions.
Spread walnuts on a baking sheet and place in oven for 7-8 minutes.
Allow them to cool, then rub/shake them in a clean dry towel to remove skins, then leave to cool.
Blend together the walnuts, butter, oil and garlic until they are reduced to a smoothish paste, transfer to a bowl, stir in half the cheese and season to taste.
Stir 6 tablespoons of boiling salted water into the walnut paste.
Drain the pasta, transfer to a warmed dish and mix well with the walnut paste and chopped tomato.