This is great with candied and dried fruit - cherries, dates, pineapple, raisins, apricots etc. You could also omit vanilla; substitute 2 tbsp. bourbon and swap 3/4 cup toasted chopped pecans for the dried/candied fruit.
In a large bowl, using an electric mixer on high, beat butter and sugar until light and fluffy, about 3 minutes. Beat in eggs yolks and vanilla. Reduce speed to low; add flour, baking powder, salt and dried fruit. Mix just until a stiff dough forms. Turn onto a floured work surface, cut dough into halves, and form each half into a 1½-inch thick log. Wrap in plastic and refrigerate at least 2 hours or up to 2 days.
Preheat oven to 375F and line 2 large baking sheets with parchment paper.
Cut logs into ¼-inch-thick slices and arrange about 1 inch apart on pans. Refrigerate 10 minutes, then bake until lightly browned around the edges and firm in the center, 12 to 15 minutes. Let cookies cool 5 to 10 minutes on the pan before transferring to wire racks to cool completely. Decorate with your favorite icing if desired.