Step 1

In a large pot, melt the butter over medium heat. Stir in the onion and celery, cooking until the onion is translucent and the celery begins to soften.

Step 2

Add the potatoes and carrots to the pot. Season with salt and pepper. Stir in the flour and cook for 1 to 2 minutes. Add the vegetable broth and bring to a boil. Reduce the heat to low and simmer gently until the potatoes are tender, about 45 minutes.

Step 3

Remove from the heat and stir in the milk and parsley. Continue cooking until the soup begins to bubble again. Remove from the heat, ladle into bowls, and serve.