Make the Graham Cracker Crust. Preheat oven to 325 degrees.
Place graham crackers in a food processor. Pulse until crackers are fine crumbs, about 30 seconds.
Add 1/2 cup melted butter and 2 tablespoons dark brown sugar. Pulse until combined, about 10 to 15 seconds.
Pour mixture into a nonstick 9 x 13-inch pan. Use your hands to press the mixture in an even layer along the bottom of the pan.
Place on center rack of oven and bake 5 minutes. Let cool.
Prepare Milk Chocolate Chip Cake. Keep oven temperature at 325 degrees.
Sift together flour, cocoa powder, baking powder, and salt onto a piece of parchment paper. Set aside.
Place 1 cup dark brown sugar and the 1 cup of butter cut into pieces in a mixing bowl and beat on low speed with an electric mixer for 30 seconds. Then beat on medium speed for 4 minutes. Scrape down sides of bowl.
Add 3 eggs, 1 at a time, beating on medium speed for 1 minute after each addition. Scrape down sides of bowl.
With mixer on low, add dry ingredients. Mix until incorporated.
Add 1/2 cup milk and vanilla extract. Mix on low until combined.
Add milk chocolate chips and mix on low for 10 seconds. Remove bowl from mixer and use a rubber spatula to finish mixing ingredients.
Pour batter on top of graham cracker crust and use rubber spatula to spread evenly. Bake for 42 to 45 minutes, or until toothpick inserted in center comes out clean.
Cool cake in pan for 20 minutes. Invert cake onto a baking sheet and refrigerate for 10 minutes.
Turn cake onto a cutting board, crust side down. Cut cake into 12 rectangles by cutting in half lengthwise and then making 5 cuts crosswise. You can trim the edges of the cake before you cut into rectangles to get more even looking pieces. Place cakes pieces on baking sheet and set aside.
Make Creamy Peanut Butter Filling. Place 1 1/2 cups peanut butter and 1/2 cup confectioners' sugar in the bowl of an electric mixer fitted with paddle attachment. Mix on low for 20 seconds. Scrape down sides of bowl and beat on medium-high for 3 minutes. Set aside.
Make Peanut Meringue Topping. Preheat oven to 450 degrees. Finely chop 1/2 cup peanuts using a food processor. Set aside.
Heat 1/4 cup granulated sugar, 1/4 cup light corn syrup, and 1/4 cup water in a small saucepan over medium-high heat, stirring to dissolve sugar. Bring to a boil and boil, stirring often, until temperature reaches 240 degrees. This will take about 3 minutes. Remove from heat.
Immediately place 4 egg whites in a bowl of an electric mixer fitted with a balloon whisk. Turn mixer on high until soft peaks from, about 1 minute.
Lower speed to medium and very slowly pour hot syrup into egg whites. Once all syrup has been added, increase speed to high until egg whites are stiff, about 2 minutes.
Use a rubber spatula to fold peanuts into meringue. Spoon meringue into a pastry bag fitted with a medium star tip.
Pipe a border of meringue on top of each cake piece. Fill center of border with 1 heaping tablespoon of peanut butter filling.
Pipe the rest of the meringue in lengthwise strips to cover all of the peanut butter.
Place in oven for about 3 1/2 minutes, until meringue starts to turn golden brown. Serve.