Preheat the oven to 325 degrees F. Lightly butter a 9 x 13-inch pan and line with parchment paper, allowing enough overhang on the long side to lift up the brownies.
To make the cream cheese layer: Place the cream cheese in the bowl of a mixer fitted with a paddle and beat until smooth. Add the egg yolk, sugar, flour, and vanilla, at a time, beating well after each addition. Scrape down the sides of the bowl, transfer to another bowl, and set aside. Clean the mixer.
To make the brownie layer: Place the butter and chocolate in a small saucepan over the lowest possible heat and cook, stirring, until almost all the chocolate has melted. Off heat, stir until smooth. Set aside to cool to room temperature.
Place the eggs and sugar in the bowl of a mixer fitted with a paddle and beat until lemon-colored and thick. Add the cooled chocolate mixture and vanilla and beat until well combined. Scrape down the sides of the bowl. Place the flour, baking powder, and salt in a separate bowl, mix well, and add to the chocolate mixture. If desired, add the chocolate chips and beat until well combined.
Place half the chocolate mixture in the prepared pan, then dollop the cream cheese mixture over it and don't worry if the cream cheese doesn't cover the chocolate: it won't. Top with the remaining chocolate mixture. Take a table knife and gently draw it from east to west and then from north to south, making a checkerboard pattern. Do not allow the mixtures to combine too much. Sprinkle with the nuts, if desired.
Transfer to the oven and bake until the sides, but not the top, are just beginning to brown, 25 to 30 minutes. Do not wait until a tester comes out clean: they will be overbaked at that point.
Set aside to cool for about 10 minutes, then cut into 32 bars. Cover and refrigerate.
Reprinted with permission from Cookies for Kids' Cancer: Best Bake Sale Cookbook, by Gretchen Holt-Witt, copyright (c) 2011. Published by Wiley.