Beat butter in a large mixing bowl with an electric mixer on medium speed for 30 seconds. Add brown sugar, baking powder, cinnamon, allspice, and salt. Beat until combined. Add eggs and vanilla; beat until well combined. Beat in as much of both kinds of flour as you can; stir in remaining flour with a wooden spoon. Divide dough in half. Cover and chill for 1 hour or until firm enough to handle.

Preheat oven to 375 degrees F. Roll each portion of dough on a lightly floured surface until 1/8 inch thick. Cut into shapes using 2- to 2-1/2-inch star-shape cutters. Transfer to ungreased cookie sheets. Using a 1-inch star-shape cutter, cut out centers from half of the unbaked cookies; remove centers and reroll dough to make more cookies.

Bake in preheated oven for 7 to 9 minutes or until edges are firm and bottoms are very light brown. Transfer cookies to a wire rack; cool.

Spread the bottom of each solid cookie with about 1/2 teaspoon jam. If desired, sift powdered sugar over the cookies with cutout centers. Place cookie with cutout center atop preserves, sugar side up. Store in covered container at room temperature up to 1 week. Makes about 60.