Preheat the oven to 350 degrees F. If you can fit 2 to 3 baking sheets, stacked, in your fridge, place them inside to let them chill ahead of time (optional, but a great trick).
In a medium bowl (a stand mixer works great, too), beat together the butter and sugar until light and fluffy, about 3 minutes.
Add the egg and vanilla, and beat to combine, scraping down the sides as needed, about 1 minute.
Add the flour, salt, and pumpkin pie spice, and stir until well incorporated.
Following the instructions on your cookie press, add the dough to the press.
Remove a baking sheet from the fridge, and follow the cookie press instructions to press the dough out onto the prepared sheet.
Continue pressing out the cookies so that they are about 1 1/2 inches apart and fill the pan.
Bake for 7 to 9 minutes until lightly browned around the bottom, but not at all dark. Let the cookies cool on the baking sheet for 5 minutes before removing to cool on a wire rack.
Repeat with remaining dough and un-greased, chilled cookie sheets.
Notes
If the cookie dough becomes too soft towards the end (the cookies will get really flat and look squished), press the dough onto the cookie sheets, and let the pressed cookies chill in the fridge for 10 minutes before baking.
The trick to helping them keep their shapes is chilling the baking sheets in the fridge as you prep the dough. The cold sheets will help them maintain their form when they go into the oven.
I recommend the OXO cookie press. After trying a few, this is by far the easiest to use (and it cleans up easily, too).
No cookie press? Divide the dough into 3 parts; then working with 1 part at a time, place the dough in a large piping bag with a large cupcake star tip (Wilton 1M) attached. Pipe out stars and wreaths by hand.