Peel the potatoes and quarter them. Put them in a pot of cold water with some salt and bring them to a boil. Turn down the heat to a simmer; simmer them until they're tender, 15 to 20 minutes.
Mash the potatoes; set them aside.
Clean and coarse chop the leeks.
Melt the 2 tablespoons butter in a large saute pan.
Add the leeks and sweat (slow fry) them until they are soft and translucent.
Add the chicken broth and a little salt and pepper; simmer for 3 to 4 minutes.
Cool this a bit.
Puree all the leeks in a blender or in a food processor in batches; set them aside.
In a mixing bowl, add the potatoes, leeks, sour cream, 1/2 cup butter, and milk.
Whip with a mixer. Only whip until just fully blended. Do not over beat.
Season, to taste, with salt and pepper.