Special equipment: A blender (my preference) or a food processor A pot for cooking the spaghetti
Rinse the cherry tomatoes and basil leaves and pat them dry.
Drop the tomatoes into the blender jar or food processor bowl followed by the garlic clove, the almonds, basil leaves, peperoncino and 1/2 tsp salt. Blend for a minute or more to a fine puree; scrape down the bowl and blend again if any large bits or pieces have survived.
With the machine still running, pour in the olive oil in a steady stream, emulsifying the puree into a thick pesto. Taste and adjust seasoning. (If you're going dress the pasta within a couple of hours, leave the pesto at room temperature. Refrigerate if you'll use it longer storage, up to 2 days, but let it return to room temperature before cooking the pasta.)
To cook the spaghetti, heat 6 quarts of water with 1 tablespoon salt, to the boil in the large pot. Scrape all the pesto into a big warm bowl.
Cook the spaghetti al dente, lift it from the cooking pot, drain briefly, and drop onto the pesto. Toss quickly to coat the spaghetti, sprinkle the cheese all over, and toss again. Serve immediately in warm bowls.