Heat oil in a large nonstick pan over medium heat. Add the sliced onions and shallots and the minced thyme. Saute until the onions become golden brown in color and begin to caramelize, about 25 minutes.
Add wine and vinegar and continue to cook the onions down, stirring occasionally, until completely caramelized, about 15 more minutes. Remove from heat and cool to room temperature.
Transfer the onion mixture to a cutting board. Mince the onions with a sharp knife. Place the minced onions in a large mixing bowl. Stir in the sour cream, Greek yogurt, chives and onion powder. Mix well.