Separate the cloves from the head of garlic and stew (rather than fry) in oil for 1 hour over a very low heat, at less than 212 degrees F. Remove from the heat, drain and use to garnish. Beat the egg yolks with a whisk in a thick-bottomed pan over a low heat until they double in size. Trickle in half of the oil used to cook the garlic (it should be almost cold) to make a mayonnaise-like emulsion. Season the hake with salt and pepper. Place in a greased ovenproof dish and cover with the garlic emulsion. Bake in the oven for 6 minutes until golden.
Garlic oil sauce: Fry the thinly sliced garlic, remove from the heat and add the paprika. Leave to stand then strain off the oil, leaving behind the sediment.
Chive sauce: Wash the chives and parsley, drain, then blend with the oil, sugar and salt.
Black olive sauce: Blend the pitted black olives with the capers, olive oil and garlic.
Spoon a little of each sauce onto the plates, then top with the golden hake fillets fresh from the oven.