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Combine 2 teaspoons garlic, 1 teaspoon pepper, 14⁄ teaspoon salt, and arugula in a large bowl; toss well.
Bring 4 quarts water to a boil in a large Dutch oven. Add pasta, and cook 10 minutes or until al dente; drain. Add hot pasta to arugula mixture, and toss well until arugula wilts.
Heat a large skillet over mediumhigh heat. Add oil to pan; swirl to coat. Add shrimp, remaining 1/4 teaspoon salt, and remaining ¼ teaspoon pepper, and sauté 1 minute. Add remaining 1 teaspoon garlic and shallots, and sauté 1 minute or until shrimp are done. Remove shrimp from pan. Add broth and juice to pan, scraping pan to loosen browned bits; cook 5 minutes or until liquid is reduced by half. Return shrimp to pan. Remove from heat, and stir in butter.
Arrange 11⁄2 cups pasta mixture on each of 4 plates. Spoon 1⁄3 cup shrimp mixture over each serving. Top each serving with 2 tablespoons cheese.