While you're waiting for the pasta water to boil, prepare all your vegetables and make the dressing. Mince the garlic cloves finely and mince the shallot into small pieces—I like to do this by hand for better control over the size. In a medium bowl, whisk together the Greek yogurt, olive oil, red wine vinegar, minced garlic, minced shallot, Italian seasoning, salt, and black pepper until smooth and well combined. Taste the dressing and adjust seasoning if needed, then set aside at room temperature.
While the dressing sits, prep all your vegetables to ensure they're ready when the pasta finishes cooking. Dice the bell pepper into 1/2-inch pieces for uniform crunch, dice the cucumber into similar-sized pieces, slice the grape tomatoes lengthwise in half, and drain and slice the black olives into 1/4-inch rounds. Chop the fresh parsley and cut the mozzarella into bite-sized cubes or small pieces. I find it helpful to keep the vegetables in separate bowls at this stage so nothing gets mushy while waiting for the pasta.
Bring a large pot of salted water to a boil and add the pasta. Cook according to package directions until al dente—this is important because the salad will sit for a while and you don't want mushy pasta. Drain the pasta thoroughly in a colander, then spread it out on a sheet pan or in a large bowl to cool slightly so the residual heat doesn't affect the vegetables when combined.
Once the pasta has cooled to room temperature, transfer it to a large mixing bowl. Pour the dressing from Step 1 over the pasta and toss gently but thoroughly to coat every piece—I use two large spoons to fold everything together rather than stirring, which helps prevent breaking the pasta. Add all the prepped vegetables from Step 2 (bell pepper, cucumber, tomatoes, olives, and parsley) and the mozzarella cubes, then fold everything together until evenly distributed. Taste and adjust seasoning if needed.
Transfer the completed salad to a serving bowl or airtight container and refrigerate for at least 1-2 hours before serving. This allows the flavors to meld together beautifully. Before serving, give the salad a gentle stir and taste again—you may want to add a small drizzle of olive oil or a splash of red wine vinegar if it seems to have dried out during chilling, since pasta absorbs liquid over time.