Place the chopped leeks in a bowl of cold water and allow them to sit for 20 minutes. Drain thoroughly, pat them dry, and chop roughly.
Set the stockpot over medium heat and add 2 tablespoons of the olive oil. Add the onion and garlic to the hot oil and cook, stirring to ensure they do not burn, for 1 minute. Add the leeks and cook, stirring. When the onion and leeks are softened, toss in the rosemary, sage, and thyme. Cook until the herbs release their fragrance into the room, about 2 minutes. Tumble in the potatoes. Add enough water to cover by 1 inch.
Raise the heat to high and bring the soup to a boil. Cook until your pairing knife slides right through one of the potatoes, about 15 minutes. Do not overcook the potatoes or you will have watery soup. When the potatoes are done, stop whatever you are doing and puree the soup.
Puree the soup in the blender or with an immersion blender. Work in batches as necessary, pouring the remaining 2 tablespoons of olive oil into the blender while it is running. Press each batch through a fine-mesh sieve back into a large bowl. Repeat until all the soup is pureed and pour it back in the pot. (We used an immersion blender and blended right in the pot because I like to have a few chunks of potato in my soup.)
Add the cream to the soup and stir to blend. Bring the soup to a boil, then turn down the heat to medium. Simmer, stirring occasionally, for 10 to 15 minutes. Whisk in the cold butter. Taste the soup and season with salt and pepper. Remove from heat.
Ladle the soup into bowl and garnish each bowl with 1 teaspoon of the truffle honey (if using), the chives, and crushed potato chips (optional).