1. Combine flour, cornstarch and icing sugar in large bowl. Blend in butter with a wooden spoon then knead dough with hands until soft, smooth dough forms. Divide dough in half. Work cocoa into half. Wrap and chill both doughs for two hours (or freeze for 40 minutes). On sheet of waxed paper, with floured rolling pin, roll chocolate dough into a 10 X 8-inch rectangle.
2. On another sheet of waxed paper, roll plain dough to same size rectangle. Place the chocolate dough on top of the plain dough, removing paper. Starting at 10 inch side, roll dough up tightly, jelly-roll fashion. Wrap in plastic wrap and chill 2 hours or overnight until dough is firm enough to slice.
3. To Bake: Preheat oven to 350°F. Slice roll into 1/4-inch thick slices. Place on ungreased baking sheets. For lollipops, insert wooden stick into cookie.
4. Bake in center of oven for 12 to 15 minutes or until edges are just starting to brown. Cool 10 minutes on sheets, then remove and cool completely on rack.

Tip: If refrigerated dough is too hard to slice, let stand at room temperature for about 15 minutes.

For colourful pinwheels, omit cocoa. Color each half of dough with food color and use two different colours for each pinwheel.