Fill a stockpot with 6 quarts of water, cover and bring to a boil.
In a large skillet, combine the olive oil, garlic, pancetta and red pepper and cook over high heat until the garlic is golden. Add the chicken stock and bring to a boil. Lower the heat to moderately high and boil gently until the liquid is reduced by half, about 6 minutes.
Meanwhile, add 3 1/2 tablespoons salt to the boiling water and add the linguine. Cover partially until the water just returns to a boil, then uncover, stir the pasta and cook until barely al dente. Drain the linguine, reserving 1/4 cup of the pasta water.
Add the linguine to the skillet and cook over moderate heat, tossing occasionally, until al dente. Add the reserved pasta water, 1 tablespoon at a time, if the linguine seems dry. Fold in the arugula, transfer to a bowl and sprinkle with the Parmigiano. Serve immediately.
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