In a medium–large pot, add 5 cups of water, potato, onion, carrots, celery, dill, bay leaves,
peppercorns, allspice berries. Bring to boil and cook over medium heat and cook for 10-15 minutes until the potatoes and carrots are fork tender but not overcooked. With a slotted spoon, remove the potatoes and carrots from the pot, reserving the vegetable broth.
While the potatoes and carrots are cooking, bring to boil 3 cups of water in a medium-small saucepan. Add the peas and green beans and cook for about 10-15 minutes until fork tender. Strain the peas and beans.
Bring the broth to boil, add the the fish. Reduce the heat and let the fish simmer for 10-15 minutes. While the fish is cooking, dice the carrots and the potatoes. With a slotted spoon, remove the fish to a plate.
In a large bowl combine the fish, potatoes, carrots, peas, green beans, pickles, capers with ¾ cup mayonnaise.
Transfer the mixture to a long platter (preferably a fish plater), and create an oval shape.
Cover the mixture with the cucumber slices, placing them in a way to resemble fish scales. Refrigerate until ready to serve.
Notes
Note: can be done one day ahead up to step 5. Steps 6 and 7 need to be done at the day the Fish Athinaiki will be served.