In a bowl, combine the cream cheese, sour cream, and mayonnaise. Season with salt and pepper, then divide into two portions.
Mix the shredded chicken into one portion and the sliced ham into the other. These will be your two fillings.
On a platter, arrange 4 slices of sandwich bread side-by-side. Spread with the chicken cream.
Cover with another 4 slices of bread, then spread with the ham cream. Top with the remaining 4 slices of bread.
Coat the sides and top of the cake with the remaining cream cheese mixture, smoothing it out evenly.
Garnish the top of the cake with lettuce leaves, cucumber slices, tomato slices, and sliced hard-boiled eggs. Sprinkle with fresh dill.
Refrigerate the Smörgåstårta for at least 1 hour to allow the flavors to meld. Slice and serve cold.
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