I made leek and potato soup last night like this:
Gently sweat one small onion, chopped fine, in a little butter and olive oil. Let them cook for a while, maybe 5 mins, then add 3 large leeks sliced, mainly the white part but add a little bit of green. Let them cook gently for at least 10 mins without going brown.
Add two very large potatoes (like the size of a baking potato, in fact last night I used baking potatoes because I didn't have any floury ones and it came out fine), cut into smallish chunks (ie. smaller than you would do roast potatoes), 1 1/4 pints chicken stock, pepper but not salt.
Let it cook til pots are very soft and breaking up (about 30 mins? depends on potatoes).
I blended mine in the pan with hand-held blender.
Add some milk, not sure how much, 1/4pt?, or single cream, and heat through til almost simmering but not boiling. You may want to add a little bit of salt, but I found not too much because of the salt in the chicken stock.
It was bloody lovely!