Heat a large non-stick frying pan over medium high heat. Spread the walnuts in a single layer to the hot dry pan. Cook, watching frequently until the walnuts start to brown, about 4 minutes. Transfer the toasted walnuts to a baking sheet in a single layer. When the walnuts are cool, chopped them finely and then set aside.
Preheat the oven to 350 degree F. Line a baking sheet with parchment paper.
In a large bowl using an electric mixer, beat the butter and sugar until fluffy. Beat in the egg yolk and vanilla. Add the flour and beat until combined.
In a small bowl, beat the egg white with a fork. In a shallow bowl, place the finely chopped walnuts.
Shape cookie dough into 1-inch balls. Dip each ball in the egg white and then roll them in the walnuts. Place the balls on the prepared sheet. Using your thumb, press a deep indentation in the center of each ball.
Bake the cookies for 8 minutes or until set. Remove the baking sheet from the oven and fill the center of the cookies with ¼ teaspoon of the jam. Return the sheet in the oven and bake the cookies until lightly browned, about 8 to 10 minutes.
Transfer the cookies onto a wire rack to cool completely.