Using two large pots, place 1 stick butter in the largest of the two. Melt butter over medium heat and then sauté carrots until they are very tender. Add leeks to the pan and continue to sauté until they are tender. Add water by tablespoon if necessary to prevent sticking.
Meanwhile, put potatoes into the second pot with the water and gently boil them until they are tender but still retain their shape. Saving the water, remove 6 cups of the potatoes from the water and put them into a large bowl.
Temporarily remove carrots and leeks to the bowl with the potatoes, draining butter back into the large pot. Add the second stick of butter to this pot and let it melt. Add the flour to this pot and stir constantly, over low medium heat, until the roux has cooked 5-7 minutes to remove the raw flour taste. Add all of the milk at once and whisk or stir until the milk boils and is thickened.
Using a blender, food processor or inversion blender, puree the remaining potatoes in their cooking water.
Add the potato water and vegetables to the milk pot. Season with salt to taste, being careful to stir up the whole pot to distribute the salt. Season with Sunny Paris to taste. Carefully stir up the whole pot to distribute the blend. Bring the soup to a simmer and let it cook together for 10-15 minutes, stirring often.
Serve soup garnished with a sprinkle of minced parsley or chives, and a few croutons.
Simmering all of the ingredients together is important because it makes sure that the leeks are fully cooked and helps the flavors to meld.