Start by bringing a large pot of salted water to a boil. Drop in your cheese tortellini and cook them according to the package directions. Once they are done, drain them in a colander and rinse immediately with cold water.
While the pasta is cooling, get your vegetables ready. Slice the cherry tomatoes in half and dice the cucumber into small, bite-sized pieces. If the cucumber has very thick skin, you can peel it, but the skin adds a nice crunch and color to the bowl. Chop your red onion very finely so it adds flavor without being overpowering. Place all these vegetables into a very large mixing bowl.
Next, add the sliced Kalamata olives and the roasted red peppers to the bowl. If you are using roasted peppers from a jar, make sure to pat them dry with a paper towel before chopping them.
In a small glass jar or a bowl, combine the olive oil, red wine vinegar, oregano, minced garlic, salt, and pepper. Whisk the mixture vigorously until the oil and vinegar stay combined. Set the dressing aside for a few minutes to let the dried oregano soften and release its oils.
Add the cold, drained tortellini to the bowl with the vegetables. Pour about three-quarters of the dressing over the top. Use large spoons to gently fold everything together. Add the feta cheese and the fresh parsley to the bowl.
This salad tastes much better after it has spent some time in the refrigerator. Cover the bowl with plastic wrap and let it sit for at least one hour.