Use a 23cm round non-stick cake tin. Coat base with non-stick cooking spray. Sprinkle brown sugar over it; shake tin to coat evenly. Preheat oven to 180 degrees C.
Peel, core and halve the pears. Slice crosswise into 5 mm slices. Spread slices in tin, making sure the base is completely covered.
Sift flour, ginger, baking powder and bicarbonate of soda on a plate. Using an electric mixer, beat the olive oil, white sugar and lime rind in a mixing bowl. Beat in the whole egg and the egg white until the mixture is thick.
Using a rubber spatula or large metal spoon, alternately fold the flour mixture and buttermilk into the egg mixture, starting and ending with flour mixture, until just blended.
Pour batter over the pears and smooth the top, making sure pears are completely covered. Bake for 35 minutes or until a skewer inserted in the centre comes out clean. Transfer to a wire rack and leave in the tin for 10 minutes to cool. Invert onto a plate and allow to cool a little longer before slicing.