Place the salted herring fillets in a large bowl and cover them completely with cold water. Let them soak for 1 to 2 hours, changing the water once, until they reach your preferred level of mild saltiness.

While the fish is soaking, toss the thinly sliced white onion with lemon juice and sugar in a small bowl. Let the mixture sit at room temperature for 15 minutes to soften the sharp onion bite and release its sweet juices.

In a small saucepan, combine the sunflower oil, allspice berries, bay leaves, and crushed peppercorns. Warm gently over low heat for 8 to 10 minutes until the spices are highly fragrant, then remove from heat and let the oil cool completely.

Remove the herrings from the water and pat them thoroughly dry with paper towels to ensure the oil adheres properly. Cut each fillet crosswise into bite-sized pieces about 1 inch wide.

In a clean glass jar, alternate layers of the sliced herrings and the softened lemon-marinated onions until the jar is filled.

Pour the completely cooled, spice-infused oil over the layers, ensuring the herring and onions are fully submerged. Seal the jar tightly and refrigerate for at least 24 hours before serving with rye bread and fresh dill.