In a medium bowl, combine the Greek yogurt, mayonnaise, and crumbled feta cheese, stirring until smooth and well blended. Add the freshly minced garlic, red wine vinegar, lemon juice, dried oregano, salt, and pepper, whisking together until fully combined. Finish by drizzling in the extra virgin olive oil while stirring to create a creamy, emulsified dressing. I like to make this dressing first so the flavors have time to meld together while you prepare the other components.
Bring a large pot of salted water to a boil and cook the penne pasta according to package directions until al dente. Drain the pasta in a colander and rinse briefly with cool water to stop the cooking process and prevent the pasta from sticking together. Spread the pasta on a clean kitchen towel or paper towels to dry slightly while you prepare the vegetables.
While the pasta cooks, prepare all your vegetables: dice the cucumber into 1/2-inch pieces, finely dice the red onion, chop the sun-dried tomatoes into 1/2-inch strips, and halve the drained artichoke hearts. Measure out the Kalamata olives and chop the fresh dill. Having everything prepped and ready makes assembly quick and efficient.
In a large serving bowl, combine the cooled cooked pasta with the prepared artichoke hearts, Kalamata olives, sun-dried tomatoes, diced cucumber, and finely diced red onion. Toss gently to distribute all the vegetables evenly throughout the pasta.
Pour the tzatziki dressing from Step 1 over the pasta and vegetable mixture, and stir thoroughly until all components are well coated and combined. Top the salad with the additional crumbled feta cheese and the fresh chopped dill. I recommend tossing just before serving to keep the pasta tender and prevent it from becoming too soft if it sits with the dressing for too long.