Slice the green tops off the leeks and set aside.
Using a sharp knife or mandolin, thinly slice the white portion of the leek to approximately ¼ inch wide.
Using the same method as above, thinly slice the cleaned potatoes. Set aside.
Add the leek slices to a strainer and rinse thoroughly under cold water to remove dirt.
Heat the olive oil in a Dutch oven or medium heat.
Add the sliced leeks, minced garlic, and Thyme, and saute until everything is tender and golden in color.
Add the sliced potatoes, chicken stock, butter, salt, and pepper.
Bring everything to a boil, then cover, and turn the heat to low or medium/low to maintain a simmer for approximately 20 minutes or until the potatoes are fork tender.
Once everything is cooked through and tender, use an immersion blender to puree the soup until it reaches the texture you desire.
Add the sour cream and whisk until combined.
Add salt and pepper until you reach the flavor you desire.