Bring a large pot of generously salted water to a boil. Add the fresh tortellini and cook according to the package directions (usually about 3-5 minutes). Drain the pasta and immediately rinse under cold water to stop the cooking process and cool the pasta down.

In a small bowl or a glass jar with a tight-fitting lid, combine the olive oil, red wine vinegar, lemon juice, Dijon mustard, minced garlic, dried oregano, salt, and pepper. Whisk or shake vigorously until the dressing is completely emulsified and smooth.

In a large serving bowl, gently combine the cooled tortellini, diced cucumber, chopped sun-dried tomatoes, Kalamata olives, red onion, and fresh parsley.

Pour the vinaigrette over the salad ingredients. Gently toss until everything is evenly coated in the dressing. Fold in the crumbled feta cheese last so it doesn't break down completely. Serve immediately, or cover and chill for 30-60 minutes to let the flavors meld.