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1
Fill the big pot with salted water (at least 6 quarts with a tablespoon kosher salt), and heat to a rolling boil.
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2
To make the sauce: Rinse the cherry tomatoes, basil, and mint leaves, and pat dry.
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3
Put them all in the food-processor bowl along with the pine nuts, anchovies, garlic, salt, and peperoncino.
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4
Process until pureed, scraping down the work bowl as needed.
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5
With the machine running, pour in the olive oil in a slow, steady stream, forming a thick, emulsified sauce.
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6
If serving now, scrape the sauce into a warmed deep serving bowl, and stir in the whole capers.
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7
When the pasta water is boiling, drop in the spaghetti, stirring and separating the strands.
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8
Cover the pot, return the water to a boil over high heat, then set the cover ajar, and cook the pasta until al dente.
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9
While the pasta cooks, ladle some of the boiling water into the serving bowl to warm it.
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10
Scrape in the sauce, and stir in the capers.
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11
Lift the spaghetti from the pot, let drain for a moment, drop it into the bowl, and toss well, until all the strands are coated with sauce.
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12
Sprinkle over it the parsley and grated cheese, and toss again.
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13
Serve immediately, passing more grated cheese at the table.
