In a medium-sized saucepan over medium heat combine butter and chopped onion. Cook until onion becomes translucent. Add 1/4 teaspoon of salt to the onions when cooking them. Add 2 cups chopped celery to the onions and stir for a moment or two. Add 2 tablespoons of flour to the pot and cook for about a minute. Cook the flour until it becomes fragrant like pie crust.
Add about 1/2 cup of milk to the pot and stir until the soup begins to thicken. Then add another 1/2 of milk and stir until the soup begins to thicken. Add the remaining milk in 1/2 cups increments until all of the milk is used. Turn the soup down to low, and simmer for about 15 minutes or until the celery becomes soft and tender. You may want to garnish the soup with some chopped celery, or even croutons when you are ready to serve.