Boil water: Bring a large pot of salted water to a boil over high heat.
Cook pasta: Add the fusili pasta and cook according to package directions until al dente, typically 8 to 10 minutes. Drain and rinse with cool water to stop the cooking process.
Cool completely: Spread the pasta on a baking sheet or large plate and let it cool for 5 minutes before using.
Combine wet ingredients: In a small bowl or jar, whisk together the olive oil, red wine vinegar, lemon juice, and honey.
Add seasonings: Stir in the Dijon mustard, dried oregano, kosher salt, and freshly ground black pepper until well combined.
Taste and adjust: Sample the dressing and add more salt, pepper, honey, or vinegar to suit your preferences.
Combine pasta and vegetables: In a large mixing bowl, toss the cooled pasta with the diced cucumber, halved tomatoes, sliced red onion, Kalamata olives, and green olives.
Pour dressing: Drizzle the prepared dressing over the pasta and vegetable mixture and toss everything together until well coated.
Add cheese: Gently fold in the crumbled Feta cheese, reserving some for a final garnish if desired.
Garnish and serve: Top with fresh basil or mint, add an extra drizzle of olive oil if desired, and serve chilled or at room temperature.