Place the hake in a large roasting tin and scatter over the olives. Drizzle with 1 tablespoon oil, season and bake in a preheated oven, 200°C (400°F), Gas Mark 6, for 12–15 minutes until the fish is just cooked through. For the last 5 minutes of the cooking time, add the tomatoes to the roasting tin and drizzle over another tablespoon of oil.
Meanwhile, put the garlic in a small food processor with a little salt and the basil and whizz until a paste forms. Add the remaining oil, a little at a time, and whizz to incorporate.
Arrange the fish on plates with some boiled potatoes, and drizzle over the sauce to serve.