With an electric or hand mixer, cream the butter and sugar. It should be fluffy.
Mix in the egg and vanilla completely.
Add in the the flour and orange zest and mix till combined and a ball of dough comes together.
Preheat oven to 350ºF.
Chill for 30 minutes. Roll the dough out to 1/4" thickness on a lightly floured surface. If you have an embossed rolling pin, roll out the design and then cut out the shapes. These work well as 2-3" diameter cookies. If at any point the dough feels too soft, refrigerate.
Place the cut cookie dough on a cookie sheet an inch apart and bake for 10 min. Cool on a wire rack.
Notes
For an easy transfer to the fridge, use a cutting board or cookie sheet or parchment on a counter top to roll out the dough. And whenever too warm, simply transfer to the fridge for several minutes until the dough is stiff enough.