Boil a large pot of salted water. Cook pasta until al dente, about 10 minutes.
Drain pasta and rinse briefly under cool water. Shake off excess and let it cool.
Whisk olive oil, balsamic, lemon juice, garlic, oregano, salt, pepper, and red pepper flakes in a bowl.
Combine cooled pasta, tomatoes, mozzarella, red onion, and basil in a large mixing bowl.
Pour the dressing over the salad. Toss until everything is evenly coated.
Rest 10 minutes to let flavors meld. Adjust salt and pepper to taste.
Finish with Parmesan and pine nuts before serving. Serve at room temperature or chilled.