In a large bowl, with a mixer on medium speed, beat 1 cup butter and the 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.
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 12" x 15" baking sheets. Press your thumb gently into the center of each cookie to make an imprint.
Bake cookies in a 325°F regular or convection oven until lightly browned, 18 to 20 minutes; if baking two sheets at once in one oven, switch their positions halfway through baking. Let cookies cool on sheets for 5 minutes. Then, using a wide spatula, transfer to racks to cool completely.
Spoon about ½ teaspoon jam into the center of each cool cookie.
Note: Whirl the walnuts in a food processor until very finely ground, or chop very finely with a knife. The buttons are also great filled with raspberry jam.