Bring a medium-sized pot to medium heat and pour in 2 tablespoons of vegetable oil.
Place leeks and potatoes into the pot and start to sweat off the vegetables for 5 mins.
Add milk and water to the pot. Bring everything to a boil and then simmer for 25 minutes. Make sure to stir often, so the vegetables do not burn on the bottom.
Bring a small pot of water to boil, while the soup is cooking. Add the eggs and let them boil for 6.5 minutes.
Put eggs under cold running water for 3 minutes. Peel the eggs under the water.
Place all ingredients into a high-speed blender. Blend on high until a very smooth consistency.
Season the soup with salt and pepper.
Set an egg at the base of a bowl followed by a dollop of caviar. Pour hot soup into the bowl.