1. Combine 2 teaspoons garlic, 1 teaspoon pepper, 1/4 teaspoon salt, and arugula in a large bowl; toss well.
2. Bring 4 quarts water to a boil in a large Dutch oven. Add pasta; cook 10 minutes or until al dente; drain. Add hot pasta to arugula mixture, and toss well until arugula wilts.
3. Heat oil in a large skillet over medium-high heat. Add shrimp, remaining 1/4 teaspoon salt, and remaining 1/4 teaspoon pepper; sauté 1 minute. Add remaining 1 teaspoon garlic and shallots; 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; stir in butter.
4. Arrange 1 1/2 cups pasta on each of 4 plates. Spoon 1/3 cup shrimp mixture over each serving. Top each serving with 2 tablespoons cheese.