Process pesto by adding basil, 2 Tbsp. olive oil, pine nuts, parmesan cheese, and garlic, one item at a time, to a food processor, stopping to scrape bowl in between each ingredient. Set aside. Bring 2 quarts of water to a boil in a large saucepan. Add pasta. Cook 6 minutes. Add shrimp and keep boiling for 2 more minutes. While pasta is cooking, steam broccoli according to package instructions. When pasta and shrimp are done, drain and return to pan. Add pesto and broccoli. Stir well.