Whip butter and sugar with a mixer until fluffy over medium-high speed.
Add in egg and vanilla, then continue to mix until fully blended. Switch the speed to low.
Slowly add the dry ingredients until just combined.
Scrape down the sides of the bowl. Cover the bowl with plastic wrap and refrigerate the dough for at least 30 minutes.
When ready to bake the cookies, add chopped walnuts in a small bowl.
Preheat the oven to 350F. Line a large baking sheet with parchment paper or a silicone baking mat.
Scoop the dough into 1" balls. Roll between your palms to make it into an even ball. Roll in walnuts before placing the rolled dough on a baking sheet. Repeat with the remaining dough and place each ball 2" apart.
Using your thumb, press a ½” indentation in each ball.
Scoop some apricot jam (about ¾ teaspoon) into each indentation until they are slightly heaped.
Bake for 14-15 minutes or until golden brown.