In a large pot, melt the butter over medium heat. Add the chopped onion, garlic, and sliced leeks. Cook gently for about 5-7 minutes until softened but not browned.
Add the diced potatoes and broth to the pot. Taste for salt and pepper, add thyme to taste.Bring everything to a boil, then reduce the heat and let it simmer for about 20 minutes, or until the potatoes are tender. In the meantime, add water to your small pot and bring to a boil. Add your eggs and cook for aroung 5-6 min.The eggs need to be jammy and the yolk needs to flow into the soup when broken.In a small pan, cook your bacon bits until they're crispy. Once the potatoes are tender, use a hand blender or mixer to puree the soup to your desired consistency—either smooth or slightly chunky.
Stir in some boursin cheese to your taste (but not all of it) and some cream for a richer texture. Season with salt and pepper to taste.