Process bread slices in a food processor to form fine crumbs. In a small bowl, combine the bread crumbs and milk and allow to soak for 5 minutes.

Combine the milk/breadcrumb mixture with the rest of the meatball ingredients. Mix thoroughly. Refrigerate for ½ hour to allow the mixture to become stiffer. Roll the meat into small balls, placing them on a large plate or foil-lined cookie sheet as you roll them. (The size of the meatballs doesn’t matter, as long as they are all of similar size.)

In a large sauté pan or Dutch oven, heat the oil over medium-high heat. Brown the meatballs on all sides, then remove to a plate with a slotted spoon. Set aside while preparing the sauce.

Turn heat down to medium, then add butter to the pan containing the meatball drippings. Add the mushrooms to the melted butter, and cook, while stirring, until the mushrooms have cooked down. Stir the flour into the mushrooms, and cook for 1 minute.

Slowly whisk in the milk and the broth, while scraping the bottom of the pan to release the browned bits. Continue to whisk while the sauce comes to a boil. Be sure to whisk out any lumps.

After the sauce has boiled for one minute, reduce to a simmer. Add the dill, nutmeg, and salt and pepper to taste. Gently fold the meatballs into the sauce. Cover the pan, with the lid slightly ajar, and allow the meatballs to simmer in the sauce for 20 minutes, or until they are completely cooked through.

Allow to cool slightly before serving.