Place the crumbled feta and Greek yogurt into a food processor or high-powered blender.
Add the minced garlic, olive oil, lemon juice, and lemon zest.
Process the mixture on high speed for approximately 2 minutes until completely smooth and aerated.
Stop to scrape down the sides of the bowl with a spatula to ensure no lumps remain.
Add the dried oregano and black pepper, then pulse 3-4 times to incorporate.
Transfer to a serving bowl and refrigerate for at least 15 minutes to allow the texture to set before serving.