Using an electric mixer, beat butter in a large bowl at medium speed until smooth and creamy, about 2 minutes.

Add sugar and salt and beat until pale and fluffy, about 2 minutes.

Add egg; beat until well blended, about 1 minute.

Reduce speed to low and beat in vanilla.

Add flour and beat on low speed just to blend.

Gather cookie dough into a ball and divide dough in half.

Form each half into a ball and flatten into a disk.

Wrap disks separately in plastic wrap and chill until firm, at least 4 hours.

Can be made 2 days ahead. Keep Chilled.

Position rack in center of oven; preheat to 350'F.

Line 2 baking sheets with parchment paper.

Working with 1 disk at a time, roll out the dough between 2 sheets of waxed paper to 1/8" thickness for smaller (2-inch) cookies and 1/4" thickness for larger (3- to 4-inch) cookies.

Using decorative cookie cutters, cut out cookies and transfer to prepared sheets, spacing 1 inch apart.

If cookies become too soft to transfer to cookie sheet, place in freezer on waxed paper for 5 minutes before continuing.

Gather scraps, roll out the dough, and cut more cookies, repeating until all dough is used.

If not icing cookies, decorate with sprinkles or other toppings as desired.

Bake 1 sheet at a time until cookies are firm on top and golden around edges, about 10-12 minutes for smaller cookies and up to 14 minutes for larger cookies.

Cool completely on a wire rack.

Decorate with Royal Icing, then sprinkles or other toppings as desired.

Let stand until icing sets.

Can be made 4 days ahead.