In a large soup pot, bring potatoes, leeks, broth, milk, salt, chopped lovage and pepper to a simmer over medium-high heat. Reduce the heat to low, partially cover, and simmer for about 25-30 minutes, until the potatoes are very tender.

Let cool until it is safe to purée the soup in a blender, or use an immersion blender. If you used an upright blender, return the soup to the pot. Add the peas and cook until heated through. Chill to room temperature and then place in the fridge until completely chilled, at least four hours. Or do like I did and serve warm! You can always try it cold the next day! Bon appétit!