Rinse the Baltic herring fillets under cold water and pat them very dry with paper towels; removing surface moisture helps the flour coat adhere and gives a crisper fry.
Season both sides of the fillets with a light sprinkle of Fine salt and a pinch of Ground white pepper.
Spread a thin, even layer of Fine rye flour on a plate and dredge each fillet, shaking off any excess so the coating is thin and even.
Pour a combination of Butter and a little Neutral oil into a large skillet and heat over medium–high heat; the oil raises the smoking point while the butter gives flavor—when the butter foams and starts to turn lightly golden, the pan is ready.
Carefully add the fillets to the hot fat in a single layer and fry undisturbed for 2–4 minutes per side (depending on thickness), until the coating is deeply golden and crisp and the fish is opaque through the center.
Transfer fried fillets to a plate lined with paper towels to drain, and sprinkle immediately with a little extra Fine salt to taste.
Meanwhile, put the Waxy potatoes in a pot of cold salted water, bring to a simmer, and cook until tender when pierced with a fork; drain and toss with a knob of Butter and a pinch of Fine salt to coat.
Serve the hot, crisp fillets alongside the buttery potatoes with a spoonful of Lingonberry jam on the side for a classic sweet-tart contrast. Enjoy immediately while hot and crispy.
