Bring a large pot of salted water to a boil. Cook pasta according to package directions until al dente. Drain and rinse under cold water to stop cooking. Set aside to cool.
While pasta cooks, shred the rotisserie chicken into bite-sized pieces, discarding skin and bones.
In a large bowl, combine the cooled pasta, shredded chicken, cherry tomatoes, cucumber, red onion, and parsley.
In a small jar or bowl, whisk together olive oil, lemon juice, Dijon mustard, minced garlic, salt, and pepper until emulsified.
Pour the dressing over the pasta mixture and toss gently until everything is evenly coated.
Taste and adjust seasoning with more salt, pepper, or lemon juice if needed. Serve immediately or refrigerate for at least 15 minutes to let flavors meld. Garnish with Parmesan if desired.
