To a medium mixing bowl, add the olives, olive brine, shallot, green onion, minced garlic, dill, rosemary, thyme, ½ tablespoon of the lemon zest, red pepper flakes, ¼ teaspoon of the salt, ¼ teaspoon of the pepper, and 1 tablespoon of the olive oil. Toss until combined and let marinate while preparing the feta.
In a food processor, add the feta, yogurt, remaining ½ tablespoon of lemon zest, remaining 2 tablespoons of olive oil, remaining ¼ teaspoon of salt, and remaining ¼ teaspoon of pepper. Process until smooth; about 1-2 minutes.
Add the whipped feta mixture to a serving bowl, cover with plastic wrap, and chill for 10 minutes in the refrigerator.
Spoon the olive mixture over whipped feta. Serve with crackers, vegetables, pita bread, or crostini. Enjoy!