Bring a large pot of generously salted water to a rolling boil. Add the pasta and cook until al dente according to package directions, usually 7-9 minutes. Drain in a colander, rinse briefly with cool water to stop cooking, and spread on a baking sheet to cool. Drizzle with a tiny bit of olive oil to prevent sticking.
In a small bowl or jar, whisk together the olive oil, red wine vinegar, lemon juice, Dijon mustard, minced garlic, chopped parsley, dill, dried oregano, salt, and pepper until emulsified. Taste and adjust salt, pepper, or acidity as needed.
Place the cooled pasta in a large mixing bowl. Pour about two-thirds of the dressing over the pasta and toss well with a spatula. Let it sit for 5-10 minutes to absorb the flavours slightly.
Add the halved cherry tomatoes, diced cucumber, sliced red onion, and Kalamata olives to the pasta. Add the remaining dressing and toss gently to combine. Fold in most of the crumbled feta, reserving some for garnish.
Cover and refrigerate for at least 30 minutes (up to overnight) to let the flavours meld. Before serving, let it sit at room temperature for 10-15 minutes, toss again, and garnish with the remaining feta, fresh parsley, and an extra crack of black pepper.