Preheat the oven to 180°C (350°F/Gas 4). In a saucepan, melt the butter over low heat and whisk vigorously for a few minutes with the oil, sugar, eggs and vanilla. Remove from the heat. Combine the dry ingredients, then stir in the butter mixture.
Butter and flour a 24 cm (9½ inch) square cake tin. Pour the batter into the tin. With a wet hand, flatten and smooth the surface. Bake for about 30 minutes. The cake should be fairly firm to the touch. Allow to cool, then cut into 16 squares.