In a medium bowl, whisk the first 4 ingredients. In a large bowl using an electric mixer on medium-high, beat the butter until light and fluffy, about 2 minutes. Add the sugar; beat to blend. Beat in the egg and vanilla, then the sour cream. Add the flour mixture; beat on low until just blended. Halve the dough; shape into disks. Wrap in plastic and chill until firm, 1 1/2 to 2 hours.
Preheat the oven to 375 degrees . On a floured surface, roll out 1 dough disk about 1/8 inch thick. Cut out with cookie cutters; divide between two large parchment-lined baking sheets, spacing 1 inch apart. Re-roll scraps; cut out cookies. Repeat with the remaining dough.
Bake until the bottoms of the cookies are light golden, 6 to 7 minutes. Transfer to a rack; let cool.