In large bowl, beat butter and sugar until creamy and smooth, 2 minutes. Beat in egg and salt. On low speed, gradually beat in flour until well blended. Stir in crushed red-hot candies. Divide dough into 4 equal disks. Wrap in plastic wrap; refrigerate for at least 2 hours.
Heat oven to 375°F. Line baking sheet with nonstick foil or regular foil sprayed with nonstick cooking spray.
Place one disk on lightly floured surface; place piece of waxed paper on top. Roll out to 1/4-inch thickness. Cut into about 22 cookies using triangle template; place on baking sheets. Reroll; cut out scraps. Repeat with remaining dough, for a total of about 7 dozen cookies.
Using 3/4-inch cutter, cut out centers from cookies. Fill each center with scant 1/4 teaspoon crushed candies.
Bake in 375°F oven 6 minutes, until edges are golden. Let stand on sheets 2 minutes. Transfer to rack; let cool.