In a medium bowl, whisk together flour, baking soda, and salt. Set aside.
In a large bowl, cream together butter and granulated sugar until light and fluffy.
Beat in the egg and vanilla extract until well combined.
Gradually add the dry ingredients to the wet ingredients, mixing until just combined.
Divide the dough in half, flatten each half into a disc, wrap in plastic wrap, and chill for at least 1 hour.
Preheat oven to 350°F (175°C). Line baking sheets with parchment paper.
On a lightly floured surface, roll out one disc of dough to 0.25-inch thickness. Cut out festive shapes with cookie cutters.
Place cookies on the prepared baking sheets, about 2 inches apart.
Bake for 10-12 minutes, or until edges are lightly golden.
Let cookies cool on the baking sheets for a few minutes before transferring them to a wire rack to cool completely.
While cookies are cooling, prepare the royal icing: In a medium bowl, whisk together powdered sugar, milk, vanilla extract, and corn syrup until smooth. Add more milk a teaspoon at a time if needed to reach desired consistency.
Once cookies are completely cool, decorate with royal icing and sprinkles as desired.
Notes
Let the icing set completely before stacking or storing the cookies. Store in an airtight container at room temperature.