Start by boiling your pasta in a large pot of salted water. It should feel tender yet firm to the bite when it is done, usually taking about 8 to 10 minutes. Ensure you do not overcook it; mushy pasta will not be enjoyable in your salad.
Whisk together the red wine vinegar, lemon juice, and Dijon mustard until smooth. The tangy aroma should fill your kitchen, adding a zesty kick to the salad. Watch out for clumps; make sure everything mixes well.
Add in the sun-dried tomato oil, grated Pecorino Romano, dried oregano, and crushed red pepper flakes to the dressing. Give it a good stir. When combined, the rich scent of sun-dried tomatoes will come through. If it seems too thick, a bit of extra olive oil can help.
In a large bowl, toss the cooked pasta with artichoke hearts, sun-dried tomatoes, Gaeta olives, mozzarella, and parsley. The colors should be vibrant and inviting. Make sure everything gets a fair share; avoid clumping ingredients together.
Pour the dressing over the pasta mixture and gently toss until all the ingredients are nicely coated. The salad should look luscious and gleaming. Just be careful not to be too rough to prevent breaking up the mozzarella balls.
Let the pasta salad chill in the fridge for a good hour. This allows the flavors to mingle. Skipping this step may result in a salad that tastes a bit flat, so do not rush it!
Before serving, taste and adjust with salt and pepper, adding a squeeze of lemon juice for brightness if needed. The flavors should have developed beautifully by now. Just remember not to over-season; you can always add more but cannot take it away!