Put the cheese (in chunks) with the almonds, the garlic and the chili pepper in the food processor and chop finely. With motor running add 1,5 bunch of basil, the anchovy and about 2/3 of the cherry tomatoes. Mix everything until it resembles a puree and add two good lugs of olive oil. Taste the mixture and add seasoning if needed. Set aside for later use.
Cut the remaining tomatoes in half or quarters and put aside. In the meantime you could have cooked your rigatoni so check if they are done. Leave them to drain and keep a little bit of the cooking water separately. Put the pasta back in the hot pan and mix with the puree and stir it all together well. Add a little cooking water if it is a bit too dry or dense.
For serving put it in a large dish, shake it again and add the remaining cherry tomatoes and basil leaves to it.
Notes
Make vegetarian by removing the anchovies.
Add extra veggies by serving the trapani rigatoni with a big green salad.