Heat olive oil in a large, heavy-bottomed pot over medium-high heat. Add potatoes and leeks and season with salt and pepper.
Cook, stirring occasionally until the leeks are bright green and have begun to sweat, 5 to 8 minutes. Add vegetable broth and bring to a simmer. Simmer until the liquid has reduced a bit and the potatoes are basically falling apart, 30â€“40 minutes. With a little encouragement from your wooden (or whatever) spoon, I want you to smush the tender potatoes so that they fall apart even more (this will thicken the soup, turn it creamy and make the potatoes a nice, uneven, chunky texture).
Add the greens, stirring to wilt them into the soup.
Add the sour cream and vinegar and simmer another minute or so (adding the sour cream later in the cooking process keeps a â€œfresherâ€ sour cream flavor and prevents any curdling). Season with salt, pepper, and maybe a little more vinegar.
Ladle soup into a bowl and top with more sour cream if youâ€™re going that route. Scatter the bowl with scallion and #lotsofdill, then grind some more black pepper over the whole thing.
Original recipe called for using the entire leek, and for 1 cup of dill.