Preheat oven to 350 degrees F (175 degrees C). Lightly grease cookie sheets, or line with parchment paper.
In a large bowl, cream together butter and sugar until light and fluffy. Beat in egg yolks, vanilla, and salt. Gradually mix in flour.
Shape dough into 3/4 inch balls. Dip in lightly beaten egg whites, then roll in finely chopped walnuts. Place 1 inch apart on prepared cookie sheets. Press down center of each with thumb.
Bake for 15 to 17 minutes, or until golden brown. Cool on baking sheet for 5 minutes, then remove to a wire rack to cool completely. Just before serving, fill centers of cookies with strawberry preserves.