Heat the oil in a deep pot over medium-high heat. Add the celery and onions and saute until the veggies begin to soften, about 2 minutes. Add the potatoes and toss with a good pinch of salt. Add the chicken stock and simmer until the potatoes soften, about 20 minutes. Then add the milk and butter, and stir until the butter melts.
At this point you have a few options. If you have an immersion blender, simply stick the wand in the pot and give it a few whizzes, blending some of the soup until it's nice and creamy. You'll still want a good amount of potato chunks in the soup, so don't go overboard, like I tend to do.
You can also scoop out about 2 cups of the soup and transfer it to a blender or food processor. Blend until creamy and transfer it back to the soup pot.
Or, you can simply mash a few of the potatoes with a potato masher, leaving it on the slightly chunkier side. It's up to you!
After you've creamified it, give it another taste and add plenty of salt and pepper if needed.
Scoop out a little for the kids and keep it simple for them with shredded Cheddar and a kiss of chives! (Chives are optional, of course.) As for you, adult faces, load up your bowls with plenty of chopped bacon, Cheddar, little dollops of sour cream, sliced jalapenos and chives!