Cut the bacon into small pieces and cook in a pot over medium high heat. Once the bacon is crispy, transfer to a plate lined with paper towels.
Trim off the root ends of each leek. Then cut off the darker green part and discard. Cut the remaining pieces in half length wise. Then slice each leek into small strips.
Soak the sliced leek in a bowl of water. This will allow all of the sand from the leeks to fall to the bottom of the bowl.
Once the leek has soaked fro about 20 minutes, remove from the water using a slotted spoon and transfer to a paper towel.
Turn the pot of bacon grease to medium heat and add the garlic, making sure to stir constantly so it doesn't burn. You may need to add additional oil to the pot. It really depends on how much grease the bacon let out.
Before the garlic browns, add the leeks and oregano in. Be careful when adding the leeks into the hot oil. When the water from the leeks makes contact with the hot oil, quite a few droplets of oil will splash up.
Cook the leeks on medium low heat for about 20-25 minutes. You don't want the leeks to brown. The goal is to soften them so that they release as much moisture as possible.
Meanwhile wash, peel, and cut the potatoes into cubes.
Add the potatoes, water, and chicken broth into the bowl of leeks and cook over medium high heat until it comes to a boil. Bring the heat back to a simmer and cook for another 35 minutes.
Add the salt and blend the soup to a smooth purée using an immersion blender or hand blender.
Add the cream and white pepper and give the soup a final blend.
Serve with the reserved bacon bits and freshly chopped chives.