In a large pot over medium heat, heat the oil. Add the celery, carrots, leeks and garlic. Sprinkle a little salt over the veggies. Saute until the veggies are softened, about 8 minutes, stirring occasionally.
Add the potatoes to the veggies and stir to combine. Saute for 2 minutes. Add the vegetable broth to just cover all of the potatoes and veggies. Bring to a boil. Cover and lower heat to medium-low to keep at just a simmer. Continue to simmer until the potatoes are fork-tender (about 15-20 minutes).
Add salt and pepper to taste.
Using an immersion blender or a blender, blend the soup until creamy and smooth. (Be careful with hot soup and blenders.)
Serve and enjoy with toppings such as green onions, cheese, sour cream or greek yogurt, etc.