In a large pot over medium heat, melt 4 tablespoons of unsalted butter. Add 1 chopped medium onion, 2 diced celery stalks, and 2 chopped carrots; sauté for 5–7 minutes until softened. Stir in 2 minced garlic cloves and cook for an additional minute until fragrant.

Pour in 6 cups of chicken broth and add 2 cubed medium potatoes to the vegetable mixture. Increase the heat to bring the mixture to a boil, then reduce to a gentle simmer. Allow the soup to cook for 10–12 minutes, or until the potatoes are tender.

In a mixing bowl, combine 2 cups of all-purpose flour and 1 teaspoon of salt. In a separate bowl, whisk together 1 large egg, ½ cup of milk, and 2 tablespoons of melted butter until smooth. Gradually fold the wet ingredients into the dry ingredients, forming a soft dough.

Once the soup is simmering gently, pinch small pieces of the dough and carefully drop them into the pot. Let the dumplings cook for 8–10 minutes, or until they float to the surface and look puffy.

Reduce the heat to low and stir in 1 cup of heavy cream, 2 tablespoons of dried parsley, and 1 teaspoon of dried thyme. Simmer gently for 3–5 minutes without boiling. Adjust with salt and pepper.