Beat butter and sugar together in a large bowl with an electric mixer until light and fluffy. Beat in egg, then stir in the vanilla. Combine flour and salt in a separate bowl; add to butter mixture and mix to form a dough. Cover dough with plastic wrap and chill for at least one hour.

Preheat the oven to 400 degrees F (200 degrees C). Chill two cookie sheets.

Transfer chilled dough to a cookie press; press out onto chilled cookie sheets.

Bake in the preheated oven until lightly golden at the edges, about 8 to 10 minutes. Transfer cookies to wire racks to cool.