In a large pot, heat oil on medium heat and add chopped onion, leek, and celery. Stir from time to time until vegetables are wilted. About 5 or so minutes. Try to keep them from burning (so stir often!)
Add diced potatoes to the pot and stir from time to time for a few minutes to help develop their flavor.
Add broth and water (or one of either) and bring your temperature up to high until liquid comes to a boil.
Once liquid is boiling, add the salt, stir a couple of times, then bring the temperature back to low, cover the pot with the lid, and cook the soup for approximately 15-20 minutes, until potatoes are fork tender.
Remove about half the potatoes and set aside. Then using a high emersion blender, puree the soup until silky smooth.
Return the potatoes back to the soup, taste to make sure the salt is to your liking, and serve!