Remove the tough stems of the asparagus then cut each spear into 1-inch pieces.
Bring a large pot of salted water to a boil. Add the pasta and cook until al dente, 10 to 11 minutes, then add the asparagus to the pot and cook it with pasta for 1 more minute. Drain the pasta and asparagus then rinse it with cold water.
Transfer the pasta and asparagus to a large bowl. Stir in the onions and tomatoes. Pour the dressing over the pasta, tossing to combine, then cover the salad with plastic wrap and refrigerate it for at least 3 hours and up to overnight. When ready to serve, stir in the Parmesan cheese and enjoy cold or at room temperature.
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