Heat oven to 350°F. Work with half of cookie dough at a time; refrigerate remaining dough until needed.
On floured surface with rolling pin, roll dough to 1/4-inch thickness (about 9-inch round). Cut with floured 3-inch star-shaped cookie cutter. With 1-inch star-shaped cutter, cut out small star from center of half of the cookies. Place large stars 1 inch apart on ungreased cookie sheets. Place small stars 1 inch apart on another ungreased cookie sheet; refrigerate while baking large stars. Repeat with remaining dough.
For large stars, bake 7 to 10 minutes or until edges just begin to brown. Cool 1 minute; remove from cookie sheets. For small stars, bake 4 to 6 minutes or until edges just begin to brown. Cool 1 minute; remove from cookie sheet. Cool all cookies completely, about 15 minutes.
Spread each large whole cookie with 1 teaspoon jam. Sprinkle large cut-out cookies with powdered sugar; place over jam-topped cookies, pressing lightly. Spread half of small cookies with about 1/4 teaspoon jam. Sprinkle remaining half of small cookies with powdered sugar; place over jam-topped cookies, pressing lightly. Store between sheets of waxed paper in tightly covered container.