Preheat the oven to 350 degrees F.
Grease an 8-inch square pan with the 2 teaspoons of butter and set aside.
In a medium pot, melt the remaining stick of butter and unsweetened chocolate over medium-low heat, stirring occasionally. Remove from the heat.
In a mixing bowl, beat together the sugar and eggs. Slowly add the chocolate mixture and mix well. Sift the flour and salt into the bowl, and fold into the mixture. Fold in the vanilla and white chocolate chips, and turn into the prepared pan. Bake in the middle of the oven until risen and a tester inserted into the center comes out clean, 25 to 30 minutes. Remove from the oven and cool in the pan on a wire rack for at least 30 minutes before cutting into 2 by 4-inch rectangles.
Cut each brownie rectangle in half lengthwise. Spread bottom half with 1/2 cup of ice cream, and top with remaining brownie half. Repeat with remaining brownies and ice cream, and place in freezer to harden slightly, about 30 minutes.
Remove from the freezer and place on dessert plates. Pour Marshmallow Icing over the top, place 1 toffee shard straight up from the top brownie, and serve.
Yield: 8 servings