Heat oven to 375 degrees. 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. Bake until the apricots are tender, 25 to 35 minutes, depending on the ripeness and size of apricots. Serve with a dollop of whipped cream on the side.