1. Preheat oven to 180°C (350°F).
2. In a bowl, combine flour, baking powder and salt.
3. Using electric mixer, beat butter with sugar in another bowl. Add eggs, zest and vanilla. Beat again for 2 minutes.
4. Add the dry ingredients to the wet ingredients, alternating with the milk and oil, and stir until smooth.
5. Oil a 23-cm (9-inch) round pan and pour the mixture into it.
6. Spread apricots over mixture and sprinkle with coconut and brown sugar.
7. Bake for 40 minutes.
8. Place a sheet of aluminum foil over the cake and continue baking for 10 to 15 minutes, until a toothpick inserted in the center of the cake comes out clean. Remove from oven and let cool before removing from pan.
9. Serve with custard.