Place apricot halves in baking dish, cut side up.
Place cookies on a clean surface.
Using a rolling pin, crush the cookies into fine crumbs, and transfer to a small bowl. Add butter, brandy, and egg yolk, and, using a wooden spoon, mix to combine. Place about 1 tablespoon of the cookie mixture into the cavity of each apricot half. Serve with a dollop of whipped cream on the side, if desired.