Preheat oven to 180 degrees C. Spray a 20 cm square cake tin with vegetable oil cooking spray. Dust with flour, tap out excess.
Place peppermint lollies in a resealable plastic bag and seal. Using a hard rolling pin or meat cleaver, crush peppermints into small pieces.
On a sheet of greaseproof paper, sift together flour, cocoa, baking powder and bicarbonate of soda.
In a large mixing bowl, using an electric mixer set on high speed, beat butter and sugar until light and fluffy. Beat in egg, egg whites and peppermint flavouring essence. Gently stir in flour mixture and crushed peppermints.
Spoon mixture into prepared tin and smooth top. Bake until a bamboo skewer inserted in centre comes out almost clean, about 25 minutes. (Be careful not to overbake). Place on a wire cooling rack and cool completely. Cut into 16 squares. Sift with icing sugar.