Start by preheating your oven to 350F (175C).
Grease a 9x13-inch oven-safe baking dish with vegetable oil or softened butter.
In a large mixing bowl, combine the all-purpose flour, baking powder, and Kosher salt.
In another bowl, beat the egg yolks with half of the white granulated sugar until the mixture is light in color and has nearly doubled in volume.
Stir in the whole milk and vanilla extract.
Pour the sweetened egg yolk mixture into the dry flour mixture, and stir gently until combined and no pockets of flour remain.
Beat the egg whites in a bowl while gradually adding the remaining half cup of white granulated sugar, until egg whites are glossy and the sugar is fully blended with the egg whites.
*The egg whites should have doubled in volume at this stage after whisking. You can also use a stand mixer here if you prefer!
Fold the whisked egg white mixture into the cake batter gently, just until combined.
Pour the batter into the prepared baking dish, and spread out the top to even out the surface.
Bake for 35 to 40 minutes, or until a toothpick comes out clean when inserted into the center of the cake.
When the cake it done, remove it from the oven and let it cool in its container.
In a bowl, whisk together the sweetened condensed milk, evaporated milk, and heavy cream.
When the cake is cool, pierce the surface all over with a fork. Slowly drizzle the milk mixture over the cake, allowing it to soak in.
For the topping, mix together the peanuts, brown sugar, flour, melted butter, and instant coffee granules until well combined. Spread this mixture evenly over the soaked cake.
Return the cake to the oven, and bake for an additional 15-20 minutes, or until the topping is golden and crispy.
Let the cake cool completely, then refrigerate for at least an hour before serving.