Melt butter in a large pot over medium heat.
Add leeks and season to taste with salt and pepper; cook and stir until leeks are tender, about 15 minutes.
Stir cornstarch into broth; pour broth into pot.
Add potatoes and bring to a boil.
Stir in cream; reduce heat and simmer until potatoes are tender, about 30 minutes.
Check seasoning before serving.
