Make the yogurt sauce. In a bowl, mix together the Greek yogurt, garlic, and fresh dill (if using), and spoon into a serving dish. Season to taste with salt and pepper and set aside.
Make the eggs. Fill a small pot with water (enough for an egg to be fully submerged), add the white vinegar, and bring to a boil. In the meantime, crack the eggs over a fine mesh sieve, one at a time, to discard the loose egg whites (this step is optional). Place the eggs into a ramekin or small bowl until ready to cook.
Once ready, reduce the heat of the water to medium-low; it should be steaming, not boiling during the cooking process. Stir the water with a spoon to create a vortex. Immediately drop one egg in the center of the pot. Repeat this step with the remaining egg and cook to the desired doneness, about 3 minutes for a runny yolk and 5 minutes for a jammy yolk. To check for doneness, gently lift the egg from the water and poke it in the center—you will be able to feel the firmness of the yolk and can cook to your liking.
Once done, remove the eggs from the pot with a slotted spoon and transfer them to a paper towel to cool. Carefully set the eggs on top of the prepared yogurt.
Make the butter sauce. Place the butter or olive oil in a small saucepan over medium-low heat, until melted. Add in the spices and mix for 1-2 minutes, until warmed and lightly toasted—do not let the spices burn, or they will taste bitter. Remove the pan from the heat and immediately spoon the sauce over the eggs and yogurt.
Top the cilbir with fresh dill, salt, and pepper, then serve immediately with warm toast.