Place butter and sugar in the bowl of a large stand mixer, fitted with a paddle attachment OR in a large mixing bowl with a wooden spoon. Mix on medium speed or by hand until creamy, about 2 minutes. Add egg and vanilla, beating well until smooth.
In a separate medium bowl, combine flour, baking soda, baking powder, and salt. Fold into butter mixture until dough is just combined.
Scrape dough into a ball and wrap in plastic wrap. Refrigerate dough at least 1 hour or up to 3 days.
Preheat oven to 350F. Line two large sheet pans with parchment paper and set aside.
Turn cookie dough onto a floured surface and roll out to 1/4-inch thickness. Use a 3-inch round cookie cutter to cut out cookies. Place cookies 2 inches apart on prepared sheet pans.
Bake cookies at 350F 10-12 minutes until edges are golden-brown. Cool cookies 10 minutes on pan, then transfer to a cooling rack to cool completely.