Make the eggs. Fill a small pot with water, enough for an egg to be fully submerged. Add a tablespoon of white vinegar (not required, though it helps the eggs hold their shape), 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.
Prepare the yogurt dip. Heat the olive oil in a small saucepan over medium heat. Add the onion to the hot pan and saute until soft and translucent. Add in the minced garlic and chopped artichoke hearts and cook 1-2 minutes more. Season with salt and pepper.
Add in all of the spinach, stirring frequently until wilted. Once cooked, scrape everything into a bowl. Add the Greek yogurt and red wine vinegar to the spinach-artichoke mixture, stirring until well combined. Season to taste (if the dip is too tart, add a pinch of sugar to balance it out).
Carefully set the eggs on top of the prepared yogurt, sprinkle over the cheese, and serve warm with toasted sourdough bread.