Make shortbread dough. In a bowl of stand mixer, fitted with a paddle attachment (or you can use a hand mixer), on medium speed cream together the butter and sugar until light and fluffy, about 2 minutes. With a rubber spatula or wooden spoon, scrape down bowl as needed.
Add vanilla. Add in vanilla and beat to combine.
Add flour and salt. Add flour and salt, and beat on low speed until the dough comes together.
Chill the cookie dough. Dump your dough out onto a lightly floured surface and shape into a disc. Wrap in plastic wrap and chill for 15 minutes before rolling out and cutting.
Preheat oven and prepare pan. Position a rack in the center of your oven. Preheat oven to 350°F. Line a baking sheet with parchment paper.
Roll and cut out cookies. On a lightly floured surface, with a lightly floured rolling pin, roll out dough to ½” thick using a rolling pin. Be sure to rotate the dough after every few rolls, to ensure the dough isn’t sticking. If the dough cracks, simply press it back together. Using a cookie cutter of choice, cut out your cookies. Press scraps back together and re-roll (if dough is getting to warm or sticky, pop back into the fridge). Keep in mind the more your re-roll the scraps the dough will get tougher.
Bake cookies. Place cookies onto baking sheet, spaced about 2 inches apart. Bake in preheated oven for about 12-15 minutes.