Combine flour, baking powder, salt, and nutmeg in a bowl; mix together.

Cream butter in a large bowl using an electric blender until fluffy and lightened in color. Add sugar and cream on medium-high speed until light and fluffy, about several minutes. Mix in vanilla and orange zest. Add flour mixture in 3 batches and mix until just combined, kneading the last addition by hand. Knead in cranberries and apricots.

Divide dough in half and roll out into two 1 1/2x7-inch long logs. Wrap each log in parchment paper and refrigerate until dough is chilled, at least 4 hours.

Preheat the oven to 350 degrees F (175 degrees C). Line 2 baking sheets with parchment paper.

Remove dough from the refrigerator and cut each log into about 16 slices that are 1/3-inch thick. Place slices 1 inch apart on prepared baking sheets.