In a small bowl, add 1½ teaspoons lemon juice and ¼ teaspoon minced garlic. Combine well and set aside.
In a medium bowl, break 8 ounces feta into rough ½ inch pieces. Add water to cover, swish briefly to rinse. Transfer to a fine mesh strainer and drain well.
In a food processor, add 8 ounces feta, 3 tablespoons milk, and 1½ teaspoons reserved lemon juice mixture. Process for 15 seconds or until mixture resembles ricotta cheese.
With food processor running, slowly drizzle in 2 tablespoons olive oil. Continue to process until mixture has a Greek yogurt consistency (some small lumps will remain) for 1½ to 2 minutes Note: stopping once to scrape down bottom and sides of the bowl.
Add 2 teaspoons of oregano. Pulse until combined.
Transfer dip to bowl: drizzle with remaining 2 teaspoons olive oil.
Note: Avoid serving with salty crackers, as the feta is already quite salty.