Bring 4 quarts water to boil in large pot. Fill large bowl with ice water. Add asparagus and 1 tablespoon salt to boiling water and cook until crisp-tender, about 2 minutes. Using slotted spoon, transfer asparagus to ice water and let cool, about 2 minutes; drain and pat dry.
Return pot of water to boil. Add tortellini and cook, stirring often, until tender. Drain tortellini, rinse with cold water and drain again, leaving tortellini slightly wet. Toss tortellini and tomatoes together in large bowl.
Whisk lemon juice, shallot, garlic, 1/2 teaspoon salt and 1/2 teaspoon pepper together in small bowl. Whisking constantly, drizzle in oil. Stir dressing into tortellini mixture, cover and let sit for 15 minutes. (Salad and asparagus can be refrigerated separately for up to 1 day; refresh salad with warm water and additional oil as needed.) Stir in asparagus, basil, Parmesan and pine nuts, and season with salt and pepper to taste before serving.