2 tablespoons butter
1/2 cup celery, finely chopped
1/2 cup onion finely chopped
2 cups potato, peeled and chopped into 3/4" squares (need not be precise)
1/2 teaspoon salt
14 ounces chicken broth
1 can condensed cream of chicken soup
1/2 cup whole milk (any milk is fine, does not have to be whole)
1/2 cup heavy whipping cream (seriously, I love this stuff. Original recipe calls for Half 'n Half. Pansy.)
In medium pot, melt butter until it heats through and almost finishes that bubbling thing it likes to do when heated pretty high. Add the celery and onion, and wilt. I have no clue what this means, so I took it to be 'cook until pretty tender'.
Add the potatoes, salt, chicken broth, and condensed soup, making sure that the potatoes are covered. They should be, otherwise you used far too many potatoes. Stir the mixture together, and bring to a boil.
Reduce the heat and simmer for 20-25 minutes, or until potatoes are cooked through. This time, it only took about fifteen minutes for mine. So, watch them. If you can stick a fork through them, you're good. You may also wish to taste test. Obey this wish, as it will tell you if you added far too much salt at a point where it can be corrected easily.
Remove between 1/2 and 3/4 of the mixture, placing it in a separate bowl. Using a Speed stick or similar utensil, puree the crap out of whatever is left in the pot. You can also use a blender, potato masher, or probably even a fork if you're desperate enough. Once you've pureed, return the stuff you set aside to the pot.
Add the milk and cream at this point, mix together and continue to heat through. Add salt and pepper to taste. This recipe makes enough for four regular servings, two large servings, or one giant serving.
Additionally, you can make fresh whipped cream to go on top so long as you don't add sugar. This means stay away from Reddi-whip and similar products. Also, crumble crisp bacon on top. Crisp bacon on this soup is awesome.
Anyway, this recipe is technically not vegetarian, since cream of chicken soup contains meat. Also, the bacon. But the bacon can be left off, not so much with the soup. As it stands, I think you might be able to make it vegetarian by using a cream of (insert non-meat thing here) soup, but I don't really want to muck with this recipe more than I already have.