Add ¼ cup sea salt in a large bowl then fill with cool tap water, enough to submerge the fish. Stir to dissolve the salt then add the fish. Swirl a few times. Clean the fish** (see notes) one at a time while the rest is submerged in salted water. Onced cleaned, rinse 2 more times in clean salted water (another bowl of water with ¼ cup of salt). Drain well in paper towels.
Transfer the cleaned fish in a large food container (with lid). In a small bowl, mix brown sugar and 4 teaspoons sea salt. Sprinkle over the herring (also inside the fish). Drizzle the liquid smoke evenly, turn the fish to completely coat. Cover and refrigerate overnight (at least 6 hours).
Brush the steamer with oil then arrange the fish, side by side in one layer. Spoon marinade over each fish then steam on medium heat for 10 minutes. Remove the lid and let the fish cool slightly so it’s easier to handle.
Preheat the oven to 375F. Line a baking sheet with aluminum foil then brush with oil. Arrange the steamed fish on the prepared sheet. Lightly brush both sides with ¼ cup dark soy sauce mixed with a pinch of salt. Bake in a preheated 375F oven for 15 minutes, gently flipping after 10 minutes.
Store leftovers in the refrigerator or freeze in batches to enjoy later. Just thaw and fry briefly in oil before serving.