More time, more flavor:
2-3 large leeks, whites and yellows sliced into quarters, float in a big bowl of cold water, swirling around to get all the dirt & grit loose. It will sink to the bottom, so you can lift out the leeks into a colander for one more rinse. (Reserve green parts for stock)
3-4 medium Russet potatoes, roughly peeled to remove any odd bits. Leave some skin on, mom says it's good for ya! Chop into irregular soup sizes, about 1/4-1". (Reserve peels for stock)
3 TBSP butter & some olive oil, or mix & match qtys. The idea is to melt it in a big soup pot, throw in the potatoes and leeks, with enough fat matter to coat them. Saute those around, with a generous sprinkle of salt, and some dried thyme, til the leeks begin to wilt. Turn flame to super low, cover, and begin your stock.
In another large pot, put the cleaned leek greens, potato skins, and whatever nice other stock thing you have around - yesterday I threw in 5 baby carrots, a big handful of parsley, a big sprig of fresh thyme, three fat fresh sage leaves, salt & pepper, celery seeds. If you have fresh celery, please do add it! Add enough water to cover, bring to a brisk boil. Let that cook, splashing a ladle of broth into the potato-leeks if they are looking thirsty. Let the broth simmer away, reducing itself for about an hour. Press the veg with a spoon a few times to express the goodness.
Put a colander over your potato-leek pot, strain in the stock. Stir & simmer until the potatoes are to your liking. Cook it long: the potatoes fall completely to bits, creating a creamy base with no chunks. A little less: you'll have a more brothy base with potato chunks.
You could opt to add some cream at the end, which is just decadent but really unnecessary. The potatoes make such a creamy goodness all their own!
Serve hot with your favorite toast, salt and fresh pepper.
Less time, fine flavor:
Prep leeks and potatoes as above, saute with the butter/oil, salt, thyme, pepper.
Add some store-bought broth or bullion, to cover plus a bit.
Cook it on down, serve it up.