In a large bowl, cream the butter, shortening and sugar with an electric mixer. Add the egg and vanilla and beat until light. In a small bowl, stir the soda, salt and flour together. Stir the dry ingredients into the creamed ingredients until well mixed. Wrap in plastic wrap and chill the dough for at least 30 minutes.
Divide the dough in half. Wrap half in plastic wrap and return to the refrigerator. Roll out the dough to 1/8-inch thickness on a lightly floured surface. Cut cookies with a cookie cutter of any design and place on ungreased cookie sheets about 2 inches apart.
Put 1 teaspoon corn syrup and 1/4 teaspoon water into each of 4 different custard cups. Tint each of the four mixtures with food coloring. Stir each well.
Paint the unbaked cookies before baking using a small paintbrush. For more fun, press cookie dough through a garlic press to make "hair" for gingerbread figures.
Preheat the oven to 375 degrees F. Bake for 9 to 10 minutes or until cookies are lightly browned. Remove the cookies with a spatula and cool on wire rack.