Whisk together all-purpose flour and salt in a medium-sized mixing bowl. Set aside.
Beat softened butter in the bowl of a stand mixer or a large bowl with a hand mixer until light and fluffy.
Add sugar to butter and beat until combined and light in color. (About 2 minutes.) Scrape down the bowl as needed with a rubber or silicone spatula.
Add the egg to the butter and sugar mixture and mix until just combined.
Add corn syrup and vanilla to the butter, sugar and egg mixture and mix until combined.
Add the flour mixture to the batter and start mixing on low so that the flour doesn't splatter everywhere. Gradually increase the speed to medium and mix until combined and the batter comes away from the sides of the bowl.
Turn cookie dough out onto a piece of waxed paper or a floured surface, shape into a disc and cut in half.
Turn one cookie dough disc out in between two sheets of waxed paper or put onto a flour-dusted counter to roll out. (I roll my cookie dough in between two sheets of waxed paper. It makes it so much easier to roll.)
Roll out dough between the two sheets of waxed paper evenly with a rolling pin.
Put dough into the refrigerator right on the cookie sheet for 30 minutes before cutting out with cutters. If you're not using waxed paper and you're just using a floured surface, you can chill for 30 minutes and then roll out. Preheat oven to 375° F. Line two cookie sheets with parchment paper or a Silpat. (You don't have to do this step, but it just makes it easier to remove the cookies. They don't usually stick though.)
Remove dough from the refrigerator onto the counter. Remove the top piece of waxed paper.
Dip cookie cutter into flour to prevent sticking. Push cutter into the dough and wiggle the cutter around to get the shape you want.
Carefully place shapes onto prepared cookie sheet about 1 1/2 to 2 inches apart. Bake for 8-10 minutes in preheated oven until edges are just starting to brown.
Re-roll dough again and repeat the process until you've finished your cookies.
Remove cookies from the oven and let them cool on a cooling grid.
Once your cookies are cool, decorate them with your favorite royal icing or buttercream frosting and sprinkles.