Beat 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. Stir in cookie crumbs. (The more you blend the cookie crumbs into the dough, the darker it gets. If you want a lightly marbled shortbread, barely stir crumbs in; if you want a more chocolaty cookie, stir longer.)
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 48 minutes or until bottoms barely begin to brown. Cool 2 minutes on baking sheets. Remove to wire racks to cool.