Drain the feta, then crumble it into a food processor. Add the Greek yogurt, 2 tablespoons of the olive oil, the lemon juice, 1 tablespoon of the honey and the black pepper.
Pulse for 60 to 90 seconds, scraping down the bowl once or twice, until the dip is smooth and fluffy.
If the dip looks thick, add the cold water 1 tablespoon at a time and pulse until creamy.
Spoon into a shallow serving bowl and swirl the top with the back of a spoon.
Drizzle with the remaining 1 tablespoon honey and 1 tablespoon olive oil, then scatter with red pepper flakes and dill.
Serve with pita wedges, cucumber slices and carrot sticks.