Bring a large pot of lightly salted water to a boil. Cook pasta shells in the boiling water, stirring occasionally until cooked through but firm to the bite, about 8 minutes. Drain and rinse with cold water until chilled.
Combine salami, romaine lettuce, roma tomatoes, cucumber, and red onion in a large bowl; pour balsamic vinaigrette dressing over salad and toss to coat. Stuff pasta shells with lettuce mixture and sprinkle with Parmesan cheese.
