Preheat oven to 350° F. Line large baking sheets with baking parchment or silicon baking sheets.
Combine butter and sugar in a bowl. Whip with a handheld mixer or stand mixer on medium-high speed until fluffy.
Combine in egg and vanilla. Beat until fully blended.
Add dry ingredients in two additions, mixing on low speed until just combined.
Scrap down the sides of the bowl. Cover with plastic wrap and refrigerate for at least 30 minutes.
Place chopped walnuts into small bowl.
Scoop the dough into 1” balls. A round tsp scoop works well. Roll between your palms into an even ball.
Roll in walnuts before placing on baking sheet. If walnuts are having trouble sticking, they may be too big, or you can scoop up a bit of the walnuts in your palm and roll the dough between your hands. Repeat with remaining dough, placing balls 2” apart.
With your thumb (or knuckle) press a ½” indentation in each ball.
Scoop some apricot jam into each indentation until they are slightly heaped, about ¾ tsp jam.
Bake for 14-15 minutes until golden brown. If baking two sheets at once, rotate sheets halfway through the bake time and bake for an extra 1-2 minutes.