For the butter-braised cabbage: Cook the bacon in a large high-sided saucepan over medium-high heat, stirring occasionally until crisp, about 12 minutes. Using a slotted spoon, transfer to a paper towel-lined plate. Add the butter to same pan, followed by the onions. Cook until the onions begin to caramelize, 3 to 5 minutes. Add the wine, vinegar and cabbage. Cover, reduce the heat to medium and continue cooking for 30 minutes.
Remove the lid from the cabbage and continue cooking until all the liquid has evaporated. Stir the crisped bacon into the cabbage and season with salt and pepper.
For the arctic char: The secret to crispy skin is lack of moisture. Leave your fish uncovered in the fridge 10 to 15 minutes to dry out. Then dry the fish with a paper towel to remove any excess moisture. Sprinkle generously with salt and pepper.
Heat a cast-iron skillet or heavy-bottomed saute pan over medium-high heat. Add enough oil to coat. When the oil is hot, but not smoking, place the fillets skin-side down in the pan, cooking in batches if needed. Using the back of a spatula, press down hard on the fillets for at least 20 seconds to ensure that the entire skin has full contact with the bottom of the pan. This will help to achieve the crispiest skin possible.
Continue cooking until the flesh cooks and there is only a bit of pink left, 5 to 6 minutes. The skin should be pulling away from the bottom of the pan. If necessary, use a spatula to loosen the skin before flipping. Flip the fish and continue cooking for an additional 30 seconds to 1 minute before transferring to a plate to rest.
Gently remove the fish skin with a paring knife and place the skin back into the pan, flesh-side down. Fry another 1 to 2 minutes over medium-high heat. Transfer to a wire rack or a paper towel-lined plate, at which point it will harden like a super-crispy fish chip.
Serve the crisp arctic char over the butter-braised cabbage and top with the crispy fish skin.
Cook's Note: Removing your fried fish skin to a wire rack will help it harden by letting the air circulate around it.