Bring a large pot of water to a rolling boil. Add about 1 tablespoon of salt to the water.
Add the gluten-free rotini pasta to the boiling water and cook according to package directions, checking 1-2 minutes before the suggested time for al dente texture.
Drain the pasta in a colander and immediately rinse under cold running water to stop the cooking process and remove excess starch.
Transfer the cooled pasta to a large mixing bowl and toss with a small drizzle of olive oil (about 1 teaspoon) to prevent sticking.
Add the cherry tomatoes, cucumber, red bell pepper, red onion, black olives, and any optional vegetables to the bowl with the pasta.
In a small bowl, whisk together the olive oil, lemon juice, salt, and pepper until well combined. Add optional garlic and oregano if using.
Pour the dressing over the pasta and vegetables, then gently toss until evenly coated.
Add the crumbled feta cheese and gently fold it into the salad.
Sprinkle the chopped basil and optional toasted pine nuts over the top of the salad.
For best flavor, cover and refrigerate for at least 30 minutes before serving.
Just before serving, give the salad a gentle toss and taste for seasoning, adding more salt and pepper if needed.