Heat a pot of water and bring to a boil; add in the tortellini. Cook the tortellini until tender. Drain the tortellini and run cold water over them so that they don't stick.
Throw a splash of olive oil over the tortellini to ensure that the pasta pieces won't further stick to each other. Place the bowl of tortellini in the fridge, let it chill.
Next chop up the olives, tomatoes, red peppers, and mozzarella cheese. In another bowl, combined the chopped up ingredients with the capers. Next, gradually add in the chilled tortellini and thoroughly combine all the ingredients.
Slowly add in red wine vinegar to your liking and olive oil. Season with salt, pepper and parmesan cheese. Once everything is combined, serve!