Beat butter at medium speed with an electric mixer until creamy; gradually add sugar, beating well. Add eggs, 1 at a time, beating until blended after each addition. Add vanilla extract, beating until blended.
Combine flour, soda, and salt; gradually add flour mixture to butter mixture, beating at low speed until blended after each addition.
Divide dough in half; wrap each portion in plastic wrap, and chill 1 hour.
Roll half of dough to 1/4-inch thickness on a floured surface. Cut out cookies with a 2 1/2-inch round cutter, and place 1 inch apart on parchment paper-lined baking sheets.
Bake at 350° for 10 to 12 minutes or until edges begin to brown; let stand on baking sheet 5 minutes. Remove to wire racks to cool. Repeat procedure with remaining dough.