Leeks! They're one of the gentlest members of the onion family, and, paired with those beautiful potatoes you have there, make one of the most classic soups there is. If you don't have a recipe for leek and potato soup already, you'll find one in almost every cookbook, and about a bajillion on the internet. The simplest recipes call for only butter (about 3 tablespoons), leeks (cleaned and thinly sliced, white and green parts only), water, and potatoes (peeled and chopped). Usually you use 1 1/2 times as much potato as leek, so if you chop your leeks and get 1 cup, use 1 1/2 cups diced potatoes. For that amount I would use about one litre of water, and it would serve two people.
If you want to bolster your recipe with onions, shallots, garlic, white wine, different kinds of stock, cream, chopped herbs, whatever, go right ahead. Serve it cold, serve it hot, whichever you prefer. Traditional leek and potato soups are blended to a creamy consistency, but with these beautiful new potatoes, I would be tempted to leave the skins on and slice the potatoes into quarter-rounds. Kind of irreverent, and the soup wouldn't pass muster in a French restaurant, but I wouldn't want to compromise those buttery, beautiful spuds.
Oh, and you'll want to get your leeks really clean before you cook with them. They are grit-magnets. And nobody likes gritty soup. A lot of people just rinse down between the layers, but that tends to waste a lot of water. A better way is to slice your leeks (save the green tops for stock or some other use), place them in a large bowl, cover them with lots of water, swish them around and leave them about ten minutes. The dirt will settle to the bottom, and the leeks will float. Skim your clean leek slices off the top and use the water for your garden or your houseplants. No waste, and clean, tasty leeks!