In a food processor, combine the crumbled feta cheese, cream cheese, and Greek yogurt.
Add minced garlic and lemon juice to the mixture.
With the food processor running, slowly drizzle in the olive oil.
Blend until smooth and creamy, scraping down the sides as needed.
Add dried oregano, salt, and pepper to taste.
Blend for an additional 30 seconds to incorporate all flavors.
Transfer the dip to a serving bowl.
Drizzle with extra olive oil on top and garnish with fresh herbs if desired.
Serve immediately or refrigerate for later use.