Trim the green leaves from the leeks, keep the white and light green parts, cut lengthwise in half, and rinse thoroughly, then slice. Peel the onion and dice.
Melt the butter in a pot, add the onion and braise briefly, add the leeks and sauté, stirring, over medium heat for about 3 minutes.
Add the peeled and diced potatoes and sauté for about 2 more minutes, stirring occasionally.
Increase heat, pour in the hot stock, and bring to a boil. Reduce heat to low, cover, and simmer the vegetables until tender, about 15 minutes.
4 minutes before the end of cooking, add the green peas (you can set aside 2 tablespoons of peas ahead of time, steam them or cook in a small amount of water, and use for garnish).
Season the soup with salt to taste and blend with the milk and basil into a smooth cream (best using an immersion blender).
Serve with croutons, reserved peas, and a basil leaf. Can also be drizzled with heavy sour cream.
