Cook the pasta: Bring a large pot of salted water to a boil. Cook the spaghetti until just al dente.
Drain and rinse under cold water to stop the cooking and cool it down. Toss with a drizzle of olive oil so it doesn’t clump.
Make the dressing: In a jar or bowl, whisk together olive oil, red wine vinegar, lemon juice, Dijon, garlic, oregano, dried basil, red pepper flakes, honey, salt, and black pepper until emulsified.
Prep the mix-ins: Chop the tomatoes, cucumber, bell pepper, onion, olives, salami (if using), and basil. Pat the mozzarella dry.
Toss it all: In a large bowl, combine the cooled spaghetti, vegetables, olives, salami, mozzarella, and Parmesan.
Pour over most of the dressing and toss gently to coat.
Chill: Cover and refrigerate for at least 30–60 minutes. The flavors blend as it chills. Before serving, toss again and add more dressing if needed.
Finish and serve: Taste and adjust salt, pepper, and acidity.
Add a final sprinkle of Parmesan and fresh basil. Serve cold or at cool room temperature.