Bring a medium pot of water to a boil.

Meanwhile, add Greek yogurt or labneh to a medium bowl with grated garlic and lemon juice. Season with kosher salt to taste and set aside.

Working one at a time, crack each egg into a fine mesh strainer, then carefully transfer to a small bowl. Repeat with remaining eggs.

Add distilled vinegar and a big pinch of salt to boiling water, then reduce heat to medium-low.

Swirl water with a spoon to create a gentle whirlpool effect, then carefully pour egg into swirling water. Cook each egg for about 3-4 minutes, or until desired doneness. Transfer egg with a slotted spoon to a paper towel-lined plate to remove excess water and season with a pinch of kosher salt. Repeat with remaining eggs.

Meanwhile, heat olive oil, chili flakes, and paprika in a medium pan over medium-low heat. Once barely shimmering, remove from heat and set aside until ready to serve.

Spread garlic yogurt into the bottom of a shallow bowl or serving dish, then drizzle with some chili oil. Arrange poached eggs overtop and drizzle with more chili oil and a sprinkle of chopped dill and serve.