Bring a large pot of salted water to a boil. Add rotini and cook until al dente according to package directions (usually 8–10 minutes). Drain and rinse under cold water to stop cooking. Drizzle with 1 teaspoon olive oil to prevent sticking, then transfer to a large bowl.

While pasta cooks, halve the cherry tomatoes, dice the cucumber, thinly slice the red onion, and slice the olives. Chop the basil and set aside.

In a small bowl or jar, whisk together olive oil, red wine vinegar, Dijon mustard, minced garlic, oregano, salt, and pepper until emulsified. Taste and adjust seasoning.

Add tomatoes, cucumber, onion, olives, and basil to the bowl with the cooled pasta. Pour the dressing overtop and toss gently until everything is well coated. Fold in crumbled feta last to keep it from breaking.

Cover and refrigerate for at least 30 minutes to let flavors meld. Toss again before serving. Serve chilled or at room temperature, garnished with extra basil.