Cook the pasta according to the package. Once al dente, transfer to a bowl with ice water. Let the pasta rest until completely cooled, about 5 minutes. Strain the pasta and place in a large bowl.

Add the olive oil, balsamic vinegar, and dried oregano and toss well. Add ¾ of the basil and toss until combined. Season with salt and pepper to taste.

To set up a plate, place half a portion on the plate. Top with mozzarella balls and tomatoes. Cover with the other half of the pasta portion. Add additional mozzarella, tomatoes, and basil.