Whisk the dry ingredients - 3 cups flour, salt, baking powder in a small bowl.
Using a mixer on high speed, beat butter and sugar until well combined, about 3 minutes.
Add the egg, egg yolk, and vanilla; beat just to combine. Reduce speed to low and gradually add dry ingredients; mix just enough to combine.
Form dough into two ¾"-thick disks; wrap in plastic.
Chill at least 2 hours.
Preheat to 325°. Let 1 disk of dough sit at room temperature until softened slightly, about 20 minutes.
Roll out on a lightly floured sheet of parchment paper until about ¼" thick, dusting with flour as needed (if dough gets soft or sticky, chill on parchment until firm).
Cut out shapes with floured cookie cutters; transfer to parchment-lined baking sheets.
Pop the baking sheets in the fridge for 10 minutes before baking - this will help keep their shape when baking.
Bake cookies, rotating baking sheets halfway through, until edges are golden, 12–16 minutes, depending on size. Repeat with scraps and remaining dough.
Transfer to wire racks and let cool completely.