Preheat oven to 350°F (175°C). Grease an 8×8-inch baking dish.
In a bowl, mix milk + lemon juice, then whisk in eggs, sugar, vanilla, and oil until smooth.
Whisk in cocoa powder. Add flour and baking powder and whisk just until smooth.
In a small bowl, whisk milk with cornstarch until fully dissolved. Set aside.
In a saucepan over medium heat, melt the sugar until amber.
Carefully pour in water slowly (it will bubble), stirring until smooth.
Pour in the milk-cornstarch mixture and whisk while cooking until thickened.
Stir in butter, then fold in roasted peanuts.
Pour cake batter into the baking dish and bake 30–35 minutes, until set.
Spread the warm caramel peanut sauce over the baked cake. Cool, then chill for clean slicing.