In a large bowl, combine yogurt, sour cream, red wine vinegar, olive oil, garlic, salt, and white pepper. Mix until well combined. Set aside.
Cut cucumber in half and scrape out any seeds. Pat the cucumber halves dry and shred using a cheese grater. Place shredded cucumber on a flour sack towel and twist it up, squeezing out all of the liquid, until dry.
Add the shredded cucumber to the garlic yogurt mixture and mix well. Cover the bowl and chill for at least 2 hours for the flavors to develop.
Can substitute Greek yogurt for plain yogurt and leave out the sour cream, if desired.
Make the sauce the day before and store overnight, covered, in the refrigerator for the best flavor.
Store leftovers covered in the refrigerator for up to 1 week. If it's a little watery, just stir well before serving.