In the bowl of the stand mixer, cream together butter and sugar. Stir in vanilla and egg yolk, then gradually add flour and salt. Stir until well-blended. Put the egg whites in the small bowl and the nuts on the small plate.
Roll dough into 1″ balls. Dip in slightly beaten egg white, then roll in chopped nuts. Place about 1″ apart on cookie sheet.
Bake in preheated oven for about 5 minutes. Remove from oven and quickly press thumb gently on top of each cookie. Return to oven and bake about 8 minutes longer.
Remove from oven and cool on wire rack. Place a spoonful of jelly, icing, or chocolate in each thumbprint.
Cream butter, egg and salt. Add sugar until spreading consistency. (For chocolate icing, reduce confectioners sugar by 2 tablespoons whisk the rest with 2 tablespoons of cocoa powder.)