Beat butter and peanut butter at medium speed with an electric mixer until creamy; gradually add sugar, beating well. Stir in vanilla.
Combine flour and salt; gradually add to butter mixture, beating at low speed until blended.
Roll dough to 1/2" thickness on a lightly floured surface. Cut with a 2 1/2" round cutter or Christmas cookie cutter. Place 2" apart on ungreased baking sheets.
Bake at 275° for 45 minutes. Cool 2 minutes on baking sheets. Remove to wire racks to cool.
Peanut Butter-Chocolate Chip Shortbread: Stir 1/2 cup semisweet chocolate mini-morsels into the dough before rolling, cutting, and baking.