STIR flour with baking powder, spices and salt in a medium bowl.
BEAT butter with sugar in a large bowl, using an electric mixer on medium-high, until fluffy, about 3 min. Beat in eggs and rum extract. Gradually beat in flour mixture, just until combined. Gather into a ball. Divide dough in half, then shape each portion into a flat disc. Wrap separately with plastic wrap. Refrigerate until firm, 1 to 1 1/2 hours.
PREHEAT oven to 375F. Line 2 large baking sheets with parchment. Dust a rolling pin with flour. Roll out 1 disk of dough on a lightly floured surface until 1/8 in. thick. Cut into shapes with a 3-in.- round cookie cutter. Arrange cookies 2 in. apart on prepared sheets.
BAKE in centre of oven, until cookies just start to brown at the edges, 7 to 8 min. Set sheet on a rack for 5 min. Then remove cookies to a rack to cool completely. Repeat with remaining dough. Gather any dough scraps and form into a disc, then chill until firm enough to re-roll and cut. Decorate with royal icing, if desired. Cookies will keep well, stored in an airtight container at room temperature, up to 1 week. (Make Ahead Tip: Freeze dough for up to a month. Thaw dough in refrigerator overnight before using.)