Mix the potato, bread crumbs, onion, milk, and allspice with the spices and let sit for 10 minutes. Add the meat, season with salt and pepper, and mix until incorporated. Make a small meatball out of the meat mixture, fry it in a little butter, and taste. Adjust the seasoning, if necessary.
Roll the meat mixture into 1/2-inch round meatballs and place them on a wet plate. In a large skillet, fry them in butter until golden brown.
To serve, spread some of the relish on the slice of bread and top with the meatballs. Serve at room temperature.
In a food processor, combine the beets, apple, vinegar and sugar and pulse until the apples and beets are finely chopped. Transfer the mixture to a bowl and combine with the mayonnaise and allspice. Season with salt and pepper, to taste.