Ina medium bowl, whisk the flour, baking soda, and salt to combine.
Ina large bowl, cream the butter and sugar together with an electric hand mixer until light and fluffy, about 5 minutes. Add the egg and mix until fully incorporated. Add the sour cream and vanilla and mix until creamy. Add the flour mixture, a third at a time, until fully combined.
Lightly flour a work surface and turn out the dough. Press the dough together into a disc and wrap in plastic wrap. Chill for 1 hour in the refrigerator.
Preheat the oven to 300˚F. Line a baking sheet with parchment paper.
Remove the plastic wrap from the dough and lightly flour a work surface. Roll out the dough to about ½-inch thick. Cut out your desired shapes using a glass (for rounds) or cookie cutters.
Transfer the cookies to the prepared baking sheet, leaving about 1 inch in between cookies. Bake for 8 minutes, until the cookie bottoms are golden brown and the tops are pale. Let the cookies cool on a wire rack.