In a large mixing bowl beat butter with an electric mixer on medium to high speed for 30 seconds. Add sugar, baking powder, orange peel, baking soda, cardamom or nutmeg, and salt. Beat until combined. Beat in egg, sour cream, and vanilla. Beat in as much of the flour as you can with the mixer. Stir in remaining flour.
Divide dough in half. Wrap half of the dough in waxed paper or plastic wrap and refrigerate. Divide the remaining dough into 4 portions. Place each portion in a bowl. Add food coloring to each portion as desired, stirring until dough is evenly colored. Wrap each portion of dough in waxed paper or plastic wrap. Chill dough at least 2 hours or up to 24 hours.
On a lightly floured surface, form a mound by dropping small amounts of each of the dough's close together in a random pattern (use half of the plain dough and half of each of the colored doughs). Shape the mound into a ball. Cover and refrigerate; repeat with remaining doughs. On a lightly floured surface, roll 1 ball of dough to 1/8 to 1/4 inch thickness. Using 2- to 3-inch cookie cutters, cut dough into desired shapes. Place cutouts 1 inch apart on an ungreased cookie sheet. If desired, sprinkle with pearl or colored sugars. (Reroll scraps of dough only once. Overworking dough blurs the colors.) Repeat with the other ball of dough.
Bake cookies in a 375 degree F oven for 7 to 8 minutes or until edges are firm and bottoms are very lightly browned. Transfer cookies to a wire rack; cool. Makes about 54 cookies.