Wash the leeks very well because they often have dirt inside. Slice them into thin rounds. Peel and chop the potatoes into small cubes. Chop the onion finely so it cooks evenly and blends smoothly into the soup.

Place a large pot on medium heat. Add the butter and let it melt slowly. Do not rush this step. The butter should melt gently without burning, giving a soft base flavor to the soup.

Add the chopped onion into the melted butter. Stir well and cook for about five minutes. The onion should turn soft and slightly golden. This step builds the base flavor of the soup.

Now add the sliced leeks into the pot. Stir them with the onions. Cook for another five to seven minutes. The leeks will soften and release a sweet smell that makes the kitchen feel cozy.

Add the chopped potatoes into the pot. Pour in the vegetable stock. Add the bay leaf if using. Stir everything well. Bring the mixture to a gentle boil, then reduce heat and let it simmer.

Let the soup cook for about 20 minutes. The potatoes should become very soft. You can check by pressing them with a spoon. Soft potatoes will help create a smooth texture later.

Remove the bay leaf first. Use a hand blender to blend the soup until smooth. If using a regular blender, let the soup cool slightly before blending. Be careful with hot liquids.

Pour in the milk and stir gently. Heat the soup again on low heat. Do not boil after adding milk, as it can change the texture. The milk gives the soup a soft and creamy finish.

Add salt and black pepper to taste. Stir well and taste the soup. Adjust seasoning if needed. Serve hot with fresh parsley on top for a simple and fresh look.