Melt the chocolate in the microwave or over boiling water in a double boiler. Stir and allow it to cool to room temperature.
Beat butter until fluffy, add sugar, egg, melted chocolate, eggnog and rum (or vanilla extract).
Sift flour, soda, salt, nutmeg and cinnamon together.
Combine the flour mixture with the butter chocolate mixture. Mix well with an electric mixer.
Form the cookie dough into a ball, cover and chill in the refrigerator for one hour.
Heat the oven to 400 F. Drop the cookie dough by rounded teaspoonfuls onto ungreased baking sheet, leaving 2 inches space between each cookie.
Bake for 8 minutes.
Remove the cookies from the baking sheet and cool on a wire rack.
Allow to cool completely, then frost with eggnog icing.