Bring a large pot of water to a bowl and season generously with salt. Cook pasta according to package directions until al dente, about 8 minutes.
Drain the pasta and run it under cold water to stop the cooking and cool it down.
Add the cooked pasta and veggies to a serving bowl. Stir to combine.
In a medium bowl, whisk together the dressing ingredients and pour them over the pasta.
Add the mozzarella, basil, parsley, and green onions to the bowl. Gently stir until everything is coated in the dressing.
Cover the bowl with plastic wrap and chill for 2 hours or more before serving. (see note) Stir once more just before serving.
Notes
You can serve this pasta salad 10 minutes after it's been prepared if you're in a hurry, but it tastes WAY better if you let it hang out in the fridge for a couple of hours.