Wash the herring fillets and salt them well. Mix the mustard and cream in bowl and submerge the herring in the mixture. Let this stand for at least 10 minutes, and as long as an hour.
Put the oats in a food processor or blender and buzz until mostly broken up. You want some of the oats to be flour, and some to be still recognizable as oats. Put the oats in a large bowl.
Heat the oil or butter in a large frying pan over medium-high heat. Set out some paper towels nearby to allow the finished fish to drain. Dredge the herring in the oat mixture and fry until golden, about 2 to 3 minutes per side. Drain on the paper towels.
Serve with beer and mashed potatoes, champ, colcannon or just simple boiled potatoes.