Put the potatoes in a saucepan and cover with water by 1 inch; season with salt. Bring to a boil, then reduce to a simmer; cook until tender, 20 minutes. Drain and return to the saucepan.
Meanwhile, preheat the broiler. Combine the beef, sausage, breadcrumbs, egg, 1/2 cup chicken broth, 1/2 teaspoon salt and a few grinds of pepper in a medium bowl; mix with your hands until combined. Form into 12 meatballs (about 2 inches) and arrange on a rimmed baking sheet. Broil until browned, about 7 minutes.
Meanwhile, melt 1 tablespoon butter in a large pot or Dutch oven over high heat. Add the mushrooms, 1/2 teaspoon salt and a few grinds of pepper. Cook, stirring, until the mushrooms are softened, about 8 minutes. Sprinkle in the flour and stir to coat. Stir in the wine and bring to a boil. Add 1 cup chicken broth and return to a boil, then reduce the heat to medium high and add the meatballs. Simmer, stirring occasionally, while you mash the potatoes.
Add the remaining 5 tablespoons butter and 1/2 cup chicken broth to the potatoes and mash. Season with salt and pepper. Stir the parsley into the meatball mixture. Serve with the potatoes.