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1
Using electric mixer, beat butter in large bowl at medium speed until smooth and creamy, about 2 minutes.
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2
Add sugar and salt and beat until pale and fluffy, about 2 minutes.
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3
Add egg; beat until well blended, about 1 minute.
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4
Reduce speed to low and beat in vanilla.
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5
Add flour and beat on low speed just to blend.
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6
Gather dough into ball; divide in half.
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7
Form each half into ball and flatten into disk.
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8
Wrap disks separately in plastic and chill until firm, at least 4 hours.
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9
DO AHEAD: Can be made 2 days ahead.
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10
Keep chilled.
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11
Position rack in center of oven; preheat to 350F.
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12
Line 2 baking sheets with parchment paper.
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13
Working with 1 disk at a time, roll out dough between 2 sheets of waxed paper to 1/8-inch thickness for smaller (2-inch) cookies and 1/4-inch thickness for larger (3- to 4-inch) cookies.
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14
Using decorative cookie cutters, cut out cookies and transfer to prepared sheets, spacing 1 inch apart.
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15
If cookies become too soft to transfer to baking sheets, place in freezer on waxed paper for 5 minutes before continuing.
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16
Gather scraps, roll out dough, and cut more cookies, repeating until all dough is used.
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17
If not icing cookies, decorate with sprinkles or other sugar toppings, if desired.
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18
Bake 1 sheet at a time until cookies are firm on top and golden around edges, about 10 minutes for smaller cookies and up to 14 minutes for larger cookies.
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19
Cool completely on rack.
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20
Decorate with Royal Icing, then sprinkles or other sugar toppings, if desired.
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21
Let stand until icing sets.
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22
DO AHEAD: Can be made 4 days ahead.
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23
Store between sheets of waxed paper in airtight containers.
