Heat a griddle pan over medium-high heat.
Dredge fish fillets in seasoned flour and shake off any excess.
Spread a small amount of soft butter onto the flesh side of each fillet.
Place fillets butter-side down in the hot pan and cook for 5 minutes.
Turn the fish over and cook until the skin is crisp and golden.
Melt and boil the sauce butter in a separate pan.
Combine egg yolks, mustard, vinegar, and herbs in a bowl.
Slowly whisk the hot butter into the egg mixture to emulsify.
Keep the sauce warm in a heatproof bowl over hot water.
Serve the mackerel immediately with the warm sauce.