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1
Cut the cherry tomatoes in half, or, if using plum tomatoes, cut them into 1/2-inch chunks, to have 3 cups of cut-up fresh tomato.
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2
Start heating 6 quarts of water with 1 tablespoon of salt in a large pot.
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3
In the big skillet, heat the 1/4 cup olive oil, sliced garlic, and peperoncino over medium-high heat, stirring, until the garlic is sizzling and starting to color.
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4
Pour in the cut tomatoes, season with a teaspoon salt, and bring to a bubbling simmer.
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5
Cook, stirring frequently, about 3 or 4 minutes, just until the tomatoes have softened a bit and the juices are slightly thickened.
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6
Turn off the heat.
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7
When the pasta water is boiling, stir in the cavatelli or other pasta.
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8
Return to the boil, and cook for 7 to 8 minutes (or 6 minutes less than time indicated on the package), then drop all the arugula into the pot.
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9
Stir well, cover, and bring the water back to the boil rapidly.
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10
Cook pasta and arugula together for 5 minutes, or until the pasta is nearly al dente.
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11
Meanwhile, bring the cut tomatoes in the skillet back to a simmer.
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12
Lift out the pasta and cooked greens with a spider, drain for a moment, then drop into the skillet.
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13
Cook over high heat, tossing continuously, until the pan juices have thickened and nicely coat the pasta.
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14
Turn off the heat, sprinkle the grated cheese over the pasta, and toss.
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15
Drizzle on more olive oil, toss, and serve immediately in warm bowls.
