In a large bowl, beat the softened butter and sugar with a mixer until light and fluffy, about 2 minutes. Beat in the egg yolk and vanilla until smooth. (Keep the egg white in a small bowl for step 4.)

Stir in the flour and salt until a soft dough forms. In the small bowl, beat the egg white lightly with a fork until just frothy, and put the chopped walnuts in another shallow bowl.

Roll the dough into 1-inch balls. Dip each ball in the egg white, then roll it in the chopped walnuts to coat. Place the balls 2 inches apart on the prepared sheets.

Press your thumb (or the rounded back of a 1/2-teaspoon measure) firmly into the center of each ball to make a deep well.

Bake 10 minutes. The wells will have puffed up a little — gently press them down again with the measure. Spoon about 1/2 teaspoon of jam into each well; don't overfill.

Bake 4–5 minutes more, until the cookies are set and the walnuts are lightly golden and the jam looks glossy. Let the cookies cool on the pan 5 minutes — the jam is very hot — then move them to a wire rack to cool completely.