To cook the fish, place the grill pan on a medium heat and allow to become quite hot. You don’t want it smoking madly, but should see a light haze, almost like vapour, arising from the pan.
Dry the fish fillets with paper towel and dip in the seasoned flour and shake off the excess. You can skip this flouring stage if you wish. With a knife, lightly butter the flesh side of the fish fillets.
Place the fish, buttered sides down on the hot grill. The fish should sizzle immediately it hits the pan, if it doesn’t, the pan wasn’t hot enough and you need to crank up the heat immediately. If you have difficulty determining if the pan is hot enough, take one of the pieces of fish and holding it above the pan, just place a corner of the buttered side onto the grill. If it sizzles, it is fine to proceed, if it doesn’t then allow the pan to get hotter.
Let the fish cook, still on a high heat until the fish is well coloured. There should be a bit of smoke coming from the pan, but not great clouds of it, so adjust the heat accordingly. Lift the fish at one corner to check if it is golden and getting crisp. When you are confident this stage has been reached, turn the heat down a little and with the help of a fish or egg slice, turn the fish over on to the skin side. Let it continue to cook until the skin is crispy and the fish is cooked through. You will know the fish is cooked when the flesh appears to be white and creamy in colour and no longer looks translucent.
While the fish is cooking, melt the butter for the relish. Allow the butter to cool a little before stirring in the chopped herbs.
Remove the cooked fish to hot serving plates, placing them with the golden flesh side up. Place a wedge of lemon on each plate and drizzle the herb relish over. If you wish, garnish with a spring of parsley and serve immediately.