Cut leeks lengthwise, separate and clean them by rinsing under cold water.
Cut the leeks into 1/2 inch slices.
Place butter and leeks in a skillet or saucepan. Cook on medium/low heat until the leeks are tender. About 10-15 minutes.
In a large pot, add the water and potatoes. Cover and bring to a boil. Lower heat to a simmer and cook until the potatoes are soft. Drain the potato water into a separate bowl for later, if needed.
In a food processor or blender, pulse together the sauteed leeks and the cream until smooth.
Mash the potatoes with a hand masher or potato ricer. Stir in the leek and cream mixture.
Slowly pour in the potato water while stirring until it reaches desired soup cinsistency.