I'm with the French when it comes to simple vegetable soups. I feel that chix stock muddies the flavor, so I use water instead, and lots of good butter to round and smooth the flavors.
Lots of leeks, cleaned well. If they're wicked dirty, slice them into thin rings, soak them in a sinkful of water like you were washing spinach, scoop them off the top and spin them dry.
Sweat the leeks in a good size knob of butter with two nice fresh aromatic bay leaves broken in half. Don't let them brown. Some recipes call for onions too. Cook them for a while.
Peel and cube some regular old russet potatoes. Toss them in, cover with water 2 inches or so, salt and pepper to taste. Simmer gently until potatoes are tender.
If you leave the veggies whole, you've got potage Parmentier. I like to puree it and whisk in another good size knob of butter. Add cream or not at this point. I usually don't but adding cream to anything is rarely a bad idea.
If you serve the puree cold, it's vichysoisse. If you want to get fancy, whip cream until it's a soft fluffy cloud, salt it lightly, put a dollop on top on each bowl, and garnish with chives. It's springtime around the lake, baby!