Pesto is the pride of Genoa, but the combination suggested here is not specifically Genoese. Provided that you like pesto you will find the recipe an excellent one for general use.
To make the pesto, pound 2 cloves of garlic in a mortar with a handful each of fresh basil leaves and pine-nut kernels and a pinch of salt. Add gradually, while you pound, 100 grams (3½ oz) of grated Parmesan cheese (or better still, if you can get it, Sardo cheese from Sardinia) and then, gradually, 2 table-spoonfuls of olive oil, obtaining eventually the consistency of a very thick cream.
Next, start grilling 4 steaks of bream. Peel, seed and chop 2 tomatoes, and set them to cook gently with 4 chopped anchovy fillets and salt and pepper in olive oil in a large pan. Turn over the fish. After the tomato and anchovy mixture has cooked for 5 minutes stir the pesto into it and make sure that it is all thoroughly hot. Remove the fish from the grill (the steaks will have had 5 minutes on each side, which should be ample), pour the sauce over them and start eating.