Preheat the oven to 375°F. Grease a 9x13 inch baking pan. I've only tested in metal and don't recommend glass at this point. Line bottom of pan with parchment paper and grease the parchment or dust with flour.
In a small bowl, whisk together the flour, baking powder, and salt.
In a saucepan, melt the chocolate and butter with the sugar over medium-low heat. Remove from heat and stir until smooth.
In a large bowl, beat the eggs and vanilla until mixed but not frothy. Stir in the chocolate mixture and then the flour mixture until fully incorporated. Fold in the chopped walnuts.
Spread in the prepared pan. Bake for 30-35 minutes, until the edges are set and a cake tester comes out with a few crumbs attached. Let cool. The brownies should sink a bit as they cool, but when everything settles they'll be good.
Meanwhile, make the rum glaze: In a medium saucepan, melt the butter and chocolate over low heat. Sift in the confectioners’ sugar and salt. Stir in the vanilla and rum, and keep warm.
Spread the brownies with the warm rum glaze. Cut into 2-inch squares and decorate each with a walnut half. Refrigerate for 1 hour before serving.