I dont have a picture cause its like literally just vaguely greenish beige slop so its not the most photogenic, but this shit is great and easy.
Just like grab a leek and slice it up, then like half a kilo or maybe a bit more of potatoes(1.1-1.3 god blessed american pounds), you can add other shit like a couple stalks of celery if you want cause this is an anything goes kinda soup. Sometimes I use garlic but it usually doesn't provide that much flavor so I guess you'd have to use a ton for it to matter that much.
Fry the leek and whatever else you're using besides the potatoes for a little bit in some oil until you're happy with how fried they are I guess, in with the potatoes and a litre of water(about a quart I think?) plus 2 vegetable stock cubes if you use those, I usually put thyme in as well but theres probably other herbs that work.
Boil until the potatoes are cooked through and just blend it smooth with either a standing blender or an immersion blender. Most recipes call for cream at this point, I've tried it once with a vegan cream and that worked well but its probably not that necessary to have any kind of cream at all at this point frankly. I've seen recipes call for specific more creamy potatoes but Im dumb and dont know shit about different potatoes.
What is necessary IMO though that I dont usually see in recipes for this, is a glug of white vinegar or some other acidic thing to break through the richness of the potatoes and leek, keep it at a simmer and just add a bit at a time and let it fully incorporate while tasting for the desired level of acidity + salt and pepper. Its a total game changer for me cause otherwise the soup is kinda bland and you need some topping to kinda mix it up, but with the vinegar acidity it becomes a soup thats great all on its own. Having some bread or crutons with it is great too for some texture variety.
Yes, this shit is good! Definitely second the vinegar tip, I usually use Apple cider vinegar cause I like the taste and hint of sweetness, but any acidity will work wonders, even just some lemon juice. I usually do a 'classic' soup base of oil, onion, carrot, celery, garlic, and let that all fry up for like 5 min as a step 0 before doing all the other stuff.
I also like having some kinda texture to the soup; just gettin some bread for dipping is indeed good, but any kinda veg like peas or corn works too. Even more potato can work; cube them, and oven roast them at the same time with just oil and spepper at like 400 for 30 min, and get some crispy bois in there.
As another niche tip, Zucchini also works as a soup base on its own or alongside potatoes, and I'm in that area where, come fall, there's tons of zucchini being passed around for free as it grows too much all at once lol. Its less dense than potato, and more creamy; cream of zucchini soup does feel like it has full fat dairy cream in it, despite being vegan!