Cut cleaned and unpeeled potatoes into large cubes (about 1 to 1 1/2 inches). Bring water and potatoes to a low boil, cooking until the potatoes are tender.
While potatoes are cooking, place oil and onions in a skillet and cook until onions are cooked soft and translucent but not brown. Add peppers, cumin, basil and garlic and continue cooking until peppers are tender, about 6-9 minutes.
Place potatoes and three quarters of the water into a blender or food processor, reserving the remaining water. Blend until smooth.
Return processed potatoes to pot, adding peppers and milk. Use reserved water to thin the soup further if desired. Warm over low heat until it is ready to serve.