Toast the almonds in a 20 cm / 8-inch skillet over medium heat for 3 to 4 minutes, shaking the pan often, until golden and fragrant. Tip onto a plate to cool.

Bring a small pot of water to a boil, score an X on the base of each tomato, and blanch for 30 seconds. Transfer to a bowl of ice water, then peel off the skins.

In a food processor, pulse the garlic and cooled almonds until coarsely chopped, about 8 to 10 short pulses.

Add the peeled tomatoes, basil, and salt. Pulse in short bursts, 5 to 6 times, until you have a chunky, wet paste, not a smooth puree, stopping while you can still see small pieces of tomato and almond.

Scrape the pesto into a large mixing bowl. Stir in the olive oil, grated pecorino, and chili flakes by hand. Taste and adjust salt.

Bring a 6-quart / 5.5 L stockpot of water to a rolling boil and add the coarse salt. Add the busiate and cook according to the package, about 10 to 12 minutes, until al dente.

Just before draining, scoop out and reserve at least 1 cup / 240 ml of the pasta water.

Drain the busiate and add it directly to the bowl with the pesto trapanese, off the heat.

Toss well, adding a splash of the reserved pasta water at a time, until the sauce coats the pasta in a loose, glossy layer.

Divide among bowls, top with extra grated pecorino, a few torn basil leaves, and a drizzle of olive oil. Serve right away.