In a small bowl, combine the cake flour and cocoa powder. Then, sift the flour mixture over a sheet of parchment paper to remove the lumps. Sifting over the parchment makes it easier to pour in later, but this is optional, so you may sift it in a separate bowl instead. Set aside for now.
Crack the eggs into a large bowl and give it a quick whisk to combine the yolks and whites before adding the granulated sugar. Whisk the eggs and the sugar together, then over a pot of boiling or hot water continue whisking until the temperature reaches 42°C/108°F. Then remove from heat.
Combine the butter, peanut butter, milk, and vanilla in a small bowl and let it sit in the water to melt while we whip the eggs. Be careful to not let water get in.
Using a hand mixer, whip the eggs on high speed for about 6-8 minutes, then lower the speed to the lowest setting and whip for 1-2 minutes. The mixture should be very light and more than doubled in size.
Sift the flour mixture again but this time evenly on top of the egg mixture. Then gently fold to combine. Be sure to scrape all the way to the bottom to get any dry flour that may have sunk, and be careful not to deflate the batter.
At this point, the peanut butter and butter should be melted. It’s okay if the peanut butter is not fully melted. Whisk the mixture a little just to combine it all, then using the same spatula you used to fold the batter, mix in about 4 tablespoons of batter into the butter mixture. Once mixed, pour evenly over the batter and fold to combine.
Prepare a cake pan lined with parchment paper. Pour the batter in a steady stream from about 30cm/1foot above the pan. Drop the pan onto the surface twice to pop any large air bubbles. Bake at 170°C/338°F for 30 minutes. When the cake is done baking, turn it out onto a cooling rack and let it cool completely.
While the cake is cooling, prepare the simple syrup. Simply combine the water and sugar in a pot and heat until the sugar has dissolved. Set aside to cool.