Preheat oven to 350 degrees F. Grease and flour a 10x15 inch pan. If halving the recipe, use a 9 inch square metal pan. You can also quarter the recipe and use a ⅛ sheet pan.
Whisk together the flour, baking powder and salt; set aside. Also, combine your milk and cut up pieces of butter in a microwave-safe cup so they'll be ready to go!
In a mixing bowl, using an electric mixer, begin beating the eggs on medium speed. Gradually add the sugar, increasing speed of mixer a bit and beating until mixture is thick and lemon colored. Beat in the vanlila.
Add the flour mixture and stir by hand or using lowest speed of mixer until fully blended. Don’t over-beat.
Heat the milk and butter in the microwave just until it begins to boil. This won't take long, so watch carefully! Pour the hot milk into the batter and stir by hand or beat on very low speed until blended and smooth.
Pour batter into the prepared pan and spread evenly.
Bake on center rack for 20 to 25 minutes (20 if halving), or until a toothpick inserted into the center of the cake comes out clean.
Drop dollops of peanut butter all over the still-warm cake and spread evenly to the edges. Let cool at room temperature for about 20 minutes, then refrigerate to set the peanut butter (about 1 hour).
In a microwave-safe dish, melt chocolate (for milk chocolate, I use a lower setting) and spread evenly over peanut butter layer. Refrigerate to allow chocolate to harden, but be careful because if the chocolate hardens too much it will crack when you slice the cake. Refrigerate it just until firm or you could even let it set at room temperature, which of course takes longer and which I very seldom do since I am so impatient!
Slice into bars.