Slice leeks up until green tips. Wash sliced leeks throughly, make sure to get sand and dirt out between layers. Roughly chop carrots. Finely chop pepper and garlic cloves.
In a large deep pot, heat over medium high heat. Add butter. When melted, add chopped leeks, carrots, garlic, along with ground black pepper to taste (used about a T of pepper). Saute, stirring occasionally until leeks become translucent (about 8 minutes).
While leek mixture is cooking, peel and roughly chop potatoes. Once leeks are cooked, add potatoes, chicken broth, bay leaves and thyme to pot. Bring to a boil and then reduce to simmer. Simmer for 20 minutes (or until potatoes are fork tender).
Remove bay leaves and thyme sprigs. Using an immersion blender (or if you don't have one, a food processor or blender will work), blend mixture until smooth. Pour in and incorporate heavy whipping cream. Stir everything until well combined. Now salt to taste. Serve soup hot or cold and top with crumbled cooked bacon, drizzle of sour cream, or small thyme sprigs.