Pour 12 cups water into a saucepan, add the vinegar and 1/2 tsp salt, bring to a boil over high heat, then reduce to a gentle simmer. One at a time, crack the eggs into a bowl and gently add to the water, keeping the yolks intact. Poach for 3 minutes, making sure the eggs do not touch one another - you should be able to poach 4 at a time. Remove this batch from the pan with a slotted spoon and place directly into serving bowls. Poach the second batch.
To make the yogurt sauce, mix the yogurt, garlic and 1/4 tsp salt in a separate bowl.
To make the dressing, heat the oil in a small saucepan over medium heat, add the red pepper flakes and cook for 5 seconds.
Pour the yogurt sauce over the poached eggs, then drizzle with the dressing and serve.
