Combine sugar and shortening in large bowl. Beat at medium speed of electric mixer until well blended. Add eggs, syrup, and vanilla. Beat until well blended and fluffy.
Combine 3 cups flour, baking powder, baking soda, and salt. Add gradually to creamed mixture at low speed. Mix until well blended.
Divide dough into 4 quarters. Wrap each quarter of dough with plastic wrap. Refrigerate at least 1 hour. Keep refrigerated until ready to use.
Heat oven to 375ºF. Place sheets of foil on countertop for cooling cookies.
Spread 1 tablespoon or more of flour on large sheet of waxed paper. Place one quarter of dough on floured paper. Flatten slightly with hands. Turn dough over and cover with another large sheet of waxed paper. Roll dough to 1/4-inch thickness. Remove top sheet of waxed paper. Cut out with floured cutter. Transfer to ungreased baking sheet with large pancake turner. Place 2 inches apart on ungreased baking sheet. Roll out remaining dough.
Sprinkle with granulated sugar or colored sugar crystals, or leave plain to frost or decorate when cooled.
Bake one baking sheet at a time at 375ºF for 5 to 9 minutes, depending on the size of your cookies (bake smaller, thinner cookies closer to 5 minutes; larger cookies closer to 9 minutes). DO NOT OVERBAKE. Cool 2 minutes on baking sheet. Remove cookies to foil to cool completely, then frost and decorate if desired.
ULTIMATE SUGAR COOKIE VARIATION
DROP COOKIE VARIATION - Do not refrigerate dough. Drop by rounded measuring tablespoonsful of dough 2 inches apart on an ungreased baking sheet. Bake at 375ºF for 7 to 8 minutes.