Bring 4 quarts of water to a boil in a large pot. Add a tablespoon of salt and the asparagus. Cook until the asparagus is tender-crisp, about 2 to 3 minutes.

Remove the asparagus with a slotted spoon and plunge it into a bowl of ice water to stop the cooking. Once cold, drain the asparagus and pat it dry with paper towels.

Return the asparagus water to a boil and add the tortellini. Cook until the pasta is completely tender, usually a minute or two past the package directions. Drain the pasta, but do not shake the colander vigorously; leaving the pasta slightly wet helps it absorb the dressing.

Whisk the lemon juice, shallot, garlic, a pinch of salt, and a pinch of pepper together in a large bowl. Slowly stream in the olive oil while whisking constantly to create a smooth emulsion, then fold in the basil.

Add the warm tortellini and cherry tomatoes to the dressing. Toss gently to coat and let the mixture rest for 10 minutes to allow the flavors to penetrate the pasta.

Fold in the cooked asparagus, Parmesan, and pine nuts. Season with salt and pepper to taste. Serve at room temperature or chilled.