First, you're going to cut the dark green part off of the leek, then cut off the root. You'll be left with just the white part and a little bit of the lighter green part. Don't worry about cutting all the green off, it's ok to have some light green. Then, cut the leeks in half and rinse them well. Cut them in half again, down the middle, and chop them. Just like you would celery! Your pieces will be pretty small - just use my photo as a guideline!
Now that your leeks are ready, get a large pot and melt butter in it over medium heat. Once the butter has melted, add the leeks and a teaspoon of salt and cook them for 5 minutes, stirring constantly. In the last thirty seconds, add in minced garlic.
Lower the heat to medium low and cook the leeks for 25 minutes. Stir occasionally. This will get them nice and soft.
While the leeks are cooking, peel, and finely dice some yukon gold potatoes.
When the leeks are finished, add the potatoes and some chicken broth to the pot. Bring this mixture to a boil over medium high heat. Then reduce the heat to low, cover, and simmer for about 25 minutes, or longer if your potatoes are not tender.
While the soup is cooking, measure out 1 cup of half and half, take out a tablespoon of the half and half, and add in one tablespoon of lemon juice. Let this sit for at least 10 minutes.
When the potatoes are tender, remove from heat and puree the mixture using an immersion blender, or transfer the mixture to your stand blender or Vitamix. Once the mixture is smooth, add in heavy cream and the half and half lemon mixture. The half and half with lemon juice will have curdled. That's ok, because you're going to blend again until incorporated.
Taste and re-season if necessary, however, keep in mind that if you're using truffle oil, you may need less salt! I would suggest testing a bowl with the truffle oil and then adding more salt, if you would like it saltier! I like salt, but with the truffle oil, I thought it had PLENTY of flavor!