Preheat the oven to 180°C/gas mark 4. Lightly grease a 23cm cake tin and line with greaseproof paper. Place the butter and brown sugar into a large frying pan and heat until the butter has melted. Add the pineapple rings and cook for 3-4 minutes, spooning the mixture over so they are caramelised. Arrange the pineapple carefully at the bottom of the tin and then pour the remaining butter mixture over.
Cream together the butter and both sugars in a large bowl. Add the eggs, one at time, adding a spoonful of flour in between each to prevent the mixture curdling. Stir through the coconut milk.
Mix in the remaining flour and baking powder, before pouring the batter over the pineapples.
Bake for 1 hour and 15 minutes until a skewer comes out of the the middle clean. You may need to cover with a piece of greaseproof paper to prevent it browning too much towards the end. Leave to cool, then slice to serve.