Place the brill on a board and cut down the center line from head to tail.
Carve the first fillet away using the bones as a guide.
Remove the second fillet from the top side of the fish.
Turn the fish over and remove the two fillets from the underside.
Skin the fillets and trim any frill from the sides.
Season the fish fillets with salt and pepper.
Melt butter in a hot pan and fry the fillets for two minutes per side.
Whisk lemon juice into olive oil in a separate non-reactive pan.
Add tomatoes, shallot, and garlic, then warm gently over medium heat.
Stir in fresh herbs, season to taste, and spoon over the fish to serve.