In a large soup pot, melt the butter over medium heat. Add the chopped onion and sauté until soft and translucent, about 5 minutes. Add the diced potatoes and pour in the chicken or vegetable broth. Bring the mixture to a boil, then reduce the heat to a simmer. Cover and cook for 20 minutes or until the potatoes are tender.

While the potatoes cook, prepare the rivels. In a medium bowl, combine the flour, egg, and a pinch of salt. Mix the ingredients with your hands until small, crumbly pieces form. These are your rivels.

Once the potatoes are tender, use a potato masher to lightly mash some of the potatoes directly in the pot. This thickens the soup while still leaving chunks. Gradually sprinkle the rivels into the simmering soup, stirring gently to prevent clumping. Simmer for 10 minutes, stirring occasionally, until the rivels are cooked through.

Stir in the milk (or heavy cream) and heat gently, ensuring the soup does not boil. Season with salt and black pepper to taste.

Ladle the soup into bowls and serve it hot. A slice of crusty bread on the side makes it even better.