Bring a large pot of salted water to a boil. Cook the spaghetti according to package directions until al dente, about 8-10 minutes.
Drain the pasta in a colander and rinse under cold running water to stop the cooking process. Shake well to remove excess water and toss with a teaspoon of olive oil to prevent sticking.
In a large mixing bowl, combine the cooled spaghetti, cherry tomatoes, cucumber, red onion, feta cheese, and black olives.
In a small bowl, whisk together the olive oil, lemon juice, salt, and pepper to create the dressing. Add optional garlic, herbs, or Dijon mustard if desired.
Pour the dressing over the salad and toss gently but thoroughly to coat all ingredients evenly.
Taste and adjust seasoning with additional salt and pepper if needed.
Add the torn basil leaves just before serving and toss once more. Serve chilled or at room temperature.