1. In a large bowl, with an electric mixer on medium speed, beat butter and sugar until smooth. Add egg yolks and vanilla and beat until well blended. Stir in flour and salt and beat just until dough comes together.
2. In a small bowl, beat egg whites to blend. Place walnuts in another small bowl. Shape dough into 1-inch balls. Dip each in egg whites, turning to coat completely, then roll in walnuts to coat. Place about 1 inch apart on buttered or cooking parchment-lined 12- by 15-inch baking sheets. Press your thumb gently into the center of each cookie to make an indentation.
3. Bake cookies in a 325° oven until lightly browned, 18 to 20 minutes; if baking more than one pan at a time, switch pan positions halfway through baking. Let cookies cool on sheets for 5 minutes, then use a wide spatula to transfer to racks to cool completely.
4. Spoon about 1/2 teaspoon jam into the center of each cooled cookie.
Note: Nutritional analysis is per cookie.
Whirl the walnuts in a food processor until finely ground, or chop very finely with a knife. Store the buttons airtight for up to 2 days.