Preheat oven to 400°F. Toast nuts in oven to deep golden. Cool.
Bring a large pot of water to a boil.
Score an X on the bottom of the tomatoes, drop them into the boiling water for 1 minute. Remove and cold shock; drain. Peel the skins then halve and seed tomatoes.
Keep the water boiling for the pasta.
Place toasted nuts in a food processor and pulse into fine-medium bits. Add garlic, about half the oil, the sherry vinegar and basil, and pulse to combine. Add the tomatoes a few at a time and pulse – you want the sauce to remain red and not be too aerated.
(If you have a mortar and pestle, mash garlic with oil, vinegar and basil first, add nuts and grind then add tomatoes to form the pesto.)
Add pesto to a large serving bowl and stir in remaining EVOO. Season with salt and pepper to taste.
Salt boiling water heavily then cook pasta to a minute shy of al dente. Add 1 cup of the starchy cooking water to the pesto, drain pasta then toss with the pesto to combine. Top with parsley, mint and cheese.