Preheat oven to 350 F.
Cream 1 3/4 cups sugar, butter, cream cheese, baking powder, salt and extracts together until well blended. Mix in egg. Add 2 cups flour, then mix on low speed until incorporated.
Divide dough roughly in half and transfer one half to another bowl. Mix food coloring, if using, and 1/2 cup flour into half of the dough. Mix cocoa powder into other half of dough.
Put remaining 1/2 cup sugar in a small bowl. Pinch off about 1 teaspoon of green dough and roll into a small ball; repeat with remaining green dough. Do the same with the chocolate dough.
To make each cookie, line up 4 small balls in a row, alternating colors: green, chocolate, green, chocolate. Squish them all together and roll lightly into 1 big ball. Roll in sugar; place on greased baking sheet 2 inches apart.
Bake 13-15 minutes. Cool on wire rack.