Beat butter with an electric mixer until fluffy. Add sugar, beating well. Beat in egg yolk and vanilla.
Combine flour and salt; stir into butter mixture. Shape dough into 1-inch balls.
Beat egg white slightly. Dip each ball into egg white, and roll in nuts. Place 1 inch apart on an ungreased baking sheet. Press thumb deeply into center of each cookie. Bake at 350° for 10 minutes or until lightly browned. Fill center with about 1/2 rounded teaspoon preserves.