Grease a baking pan with nonstick cooking spray; set aside. For the brownie batter, melt 1/4 cup chocolate chips with butter in the microwave, about 1 1/2 minutes. Stir together until smooth and set aside. In a larger bowl, blend flour, sugar and baking soda. Stir in egg, melted chocolate mixture and vanilla; set aside.
For the meringue, in a clean dry bowl, and with clean dry beaters, beat egg whites until soft peaks form. Add sugar and vanilla and continue to beat on high until stiff peaks form. Dollop very rounded-sized tablespoons of meringue on prepared baking pan. You may need another spoon to help with transferring stiff whites to pan. Dollop a couple teaspoon-sized amounts of prepared brownie mixture into the center of each meringue mound. Place in oven, turn heat to 200-degrees F and cook 30 minutes. Turn heat off and allow filled meringues to sit in oven for 8 hours to completely dry out.
When ready to serve, melt remaining chocolate chips with milk and stir to combine. Drizzle over the top of each.
Makes about 8-12 cookies, depending on the size.