Cover the almonds with boiling water for a few minutes to loosen their skins. Allow them to cool for a few minutes then, when they are cool enough to handle, slip the skins off with your fingers. Place the almonds in a non-stick frying pan and toast them for a few minutes, stirring frequently, until they are a pale golden colour.
Peel the garlic and place in a food processor along with the basil leaves and a little coarse sea salt. Pulse two or three times in the food processor then tip into a large bowl. Pulse the almonds, again with a little salt, until they are the size of small grains of rice and add to the bowl.
Peel and de-seed the tomatoes and chop into medium-size dice. Mix the tomatoes into the basil, garlic and almonds, add the grated cheese and olive oil and combine gently but well. Taste and season with freshly ground black pepper and (only if needed) a little more salt.
Boil the pasta in the usual way according to the instructions on the packet (usually just a few minutes), and make sure to keep it very al dente, especially if you are planning to serve it at room temperature. Drain the pasta but reserve a couple of ladles of the pasta water. Tip the pasta into the bowl with the other ingredients and mix it gently but quickly, so that the melting cheese is well distributed. If necessary, add a little pasta water so that the sauce lightly coats each corkscrew of pasta.
Serve straight away, either lukewarm, or at room temperature, but don't chill in the fridge since this dulls those gorgeous aromas that make this dish a joy to eat.