Heat the olive oil in a large heavy-based frying pan and add the hake fillets, skin-side down. Cook for a minute or two until the skin is just beginning to crisp, then add half the diced butter scattered around each hake fillet and cook for another couple of minutes until the skin is crisp.
Turn the hake fillets over and cook for another 1-2 minutes until cooked through and tender. The time it takes the fish will depend on the thickness of the fillet. It is important to cook it until just opaque and flaking. To check this, gently prod the thickest part of the fish with the point of a knife and the flakes should separate easily. Transfer to warmed plates while you make the sauce.
Add the rest of the butter to the frying pan and allow it to melt over a moderate heat. When it turns to a light brown foam, quickly add the herbs and a squeeze of lemon juice, swirling to combine. Season to taste.
To serve, spoon this sauce over the hake fillets and add steamed broccoli and some crushed new potatoes. Garnish with the lemon wedges.