Add the butter to a 5-quart pot over medium to medium-high heat. Once it’s starting to melt, stir in the onion and mushrooms. Cook 5 minutes, stirring frequently.
Turn the heat down to medium and stir in the flour. Cook 30 seconds, stirring constantly. Add the chicken stock and use a wooden spoon to scrape up any brown bits that have formed on the bottom.
Stir in the potatoes, salt, black pepper, allspice, and bay leaf. Bring up to a boil, and then cover the pot, turn the heat down slightly so it doesn’t boil over, and cook until the potatoes are tender, about 10 minutes, stirring occasionally. (During this time I like to make the poached eggs.)
Remove from the heat and stir in the cream, vinegar, sugar, and dill.
Serve each bowl of soup topped with a poached egg and 1/2 teaspoon of fresh dill sprinkled on top.