Separate the herring into fillets, removing any bones. Let the processed cheese warm to room temperature. Finely chop the pickled mushrooms. Chop the dill greens and set aside a few sprigs for decoration.
Lay the herring fillets on cling film, skin side down. Cover with foil and gently pound the fillets until they are even thickness. Spread the melted cheese over the herring, reserving a small amount for the croutons. Sprinkle the chopped mushrooms and dill over the cheese.
Using the cling film, carefully roll the herring into a roll, keeping the halves together as the herring may slip on the film. Wrap the herring roll in several layers of cling film to form a sausage shape. Place in the freezer for 2 hours.
While the herring roll freezes, prepare the croutons. Cut the black bread into 1 cm thick slices. Cut out circles using a thin-walled glass, or cut off the crust and cut the bread into squares. Preheat the oven to 180 °C (350 °F). Place the bread on a wire rack and bake for 6 minutes. Turn off the oven and leave the bread inside for 2 minutes more. The croutons should have a thin crust; do not overdry them.
Remove the frozen herring roll from the freezer and cut into 1 cm thick slices with a sharp knife.
Spread a small amount of the reserved cheese on each crouton. Place a herring roll slice on top of the cheese.
Decorate each canape with a slice of tomato and a sprig of dill. Let the canapes rest for 10 minutes before serving.