In a large bowl, whisk together the red wine vinegar, lemon juice, sun-dried tomato oil, Dijon mustard, pressed garlic, dried oregano, and red pepper flakes. Let this mixture sit for a minute to allow the flavors to meld, then taste and adjust seasoning with salt and pepper. I prefer to make the dressing first so it has time to develop flavor while you prep and cook everything else.

Bring a large pot of salted water to a boil and add the pasta. Cook according to package directions until al dente (firm to the bite)—do not overcook. Drain the pasta thoroughly and rinse briefly with cool water to stop the cooking process and prevent sticking. Set aside to cool slightly while you prepare the remaining ingredients.

While the pasta cooks, cut the mozzarella into 1/2-inch cubes, slice the sun-dried tomatoes into thin strips, quarter the artichoke hearts, halve the gaeta olives, and roughly chop the fresh parsley. Chop the fresh basil and set aside separately, as fresh herbs are best added just before serving to preserve their bright flavor. Measure out the pecorino romano and have all components ready for assembly.

In a large bowl, combine the cooled pasta with the mozzarella, olives, artichoke hearts, sun-dried tomatoes, and the chopped parsley. Pour the dressing from Step 1 over the mixture and toss thoroughly until all components are evenly coated. The pasta will absorb the dressing as it sits, which is why thorough tossing at this stage is important.

Cover the salad and refrigerate for at least 1 hour before serving, which allows the flavors to meld and the pasta to absorb the dressing fully. Just before serving, stir the salad gently and taste for seasoning, adding more salt, pepper, or vinegar as needed. Fold in the fresh basil at the last moment so it maintains its vibrant color and fresh flavor.