In a 4- to 6-quart pan over high heat, bring about 3 quarts water to a boil. Add pasta and cook, stirring occasionally, until tender to bite, 7 to 12 minutes. Drain and return to pan.
Add shrimp, pesto, cream, broth, and dried tomatoes to pasta; stir over medium heat until hot and evenly incorporated, 2 to 3 minutes. Add salt and pepper to taste. Pour into serving dish or divide among individual bowls.