Boil the pasta until tender in a large amount of lightly salted water. While this occurs, heat the oil in a large skillet set over medium heat. Add broccoli, tomatoes and garlic and cook, stirring, 3-4 minutes. Add the shrimp and reduce heat to low.
When pasta is cooked, scoop out 1 cup of its cooking liquid and place in the skillet. Drain pasta and add it as well as the dill, Parmesan cheese, and salt and pepper to the skillet. Mix well and serve.
*Note: To blanch broccoli, plunge into boiling water 2 minutes. Cool in cold water, and then drain well.