Unwrap the chocolate squares and the stick of butter, then place them both in a medium-sized saucepan.
Place the saucepan on the stove top and heat over medium-low, stirring occasionally, until the chocolate and butter are melted and smooth. Set aside until cool (this will take 15 minutes or so).
Meanwhile, heat the oven to 350 degrees. Lightly grease a 13- by 9- by 2-inch rectangular baking pan or a 9- by 9-inch square baking pan (the square pan will produce thicker, more cakelike brownies).
Crack the eggs into a large mixing bowl and whisk until foamy. Pour in the sugar and brown sugar and whisk until the mixture is well combined. Whisk in the vanilla extract, then carefully add the cooled chocolate mixture and stir until thoroughly combined.
In a medium-sized bowl, stir together the flour, baking powder and salt. Add this mixture to the egg and sugar mixture and beat for about 50 strokes or until the flour has been fully incorporated and the batter is smooth.
Pour the batter into the prepared baking pan and bake for 25 to 30 minutes for the 13- by 9- by 2-inch pan, 40 minutes for the 9- by 9-inch pan. Test the brownies for doneness. Cool thoroughly in the pan.
To cut the cooled brownies into uniform squares, use a sharp knife (adults only) to first score the top in a grid pattern, then slice the brownies and remove them from the pan.
For a fun Valentine's Day presentation, stencil confectioners' sugar hearts on top of each brownie. To make a stencil, cut out a heart from the center of a piece of paper. Place the stencil on top of the brownie and sift confectioners' sugar over it. Carefully lift the paper to reveal the confectioners' sugar heart. Makes 24.