Combine sugar and cocoa powder in a large bowl; stir in melted butter until mixture is smooth. Beat in 1 egg, vanilla and salt; beat in remaining egg. Fold in flour and transfer to an ungreased 20cm (8 in) square baking tin.
Bake in the preheated oven until set in the middle, about 35 minutes. Allow to cool 10 minutes in the tin, then remove to a wire rack to cool completely.
Mix icing sugar, milk and peppermint flavouring in a bowl until smooth. Spread icing over cooled brownies; spread evenly and allow to set, about 30 minutes. Cut into 16 pieces.