How To Make Potato Leek Soup Warm up some olive oil in a big pot. Cut up the two leeks and add them to the pot with the olive oil. Add the diced large potato to the pot and cover with beef broth. Cover with lid and cook on low for 30 minutes, stirring often. Once cooked, add milk and cheese (gradually) and blend with a handheld blender. Season to taste with salt, pepper and garlic powder. Serve with a drizzle of olive oil, more grated Parmesan and croutons.