Whip the eggs with the sugar using a mixer until thick, pale and very fluffy, forming stiff peaks.
In a separate bowl, whisk together the flour, cocoa powder and baking powder. Gently fold this dry mixture into the egg mixture with a spatula, working from bottom to top so you keep as much air as possible.
Add the oil and milk to the batter and fold them in with a spatula until fully combined.
Pour the batter into a 6-inch (16 cm) springform pan lined with parchment paper and bake at 350°F (180°C) for 40–50 minutes, until a toothpick comes out clean.
For the white cream: in a bowl, beat the cold heavy cream with the cream cheese and powdered sugar until smooth, thick and spreadable.
For the caramel cream: in a saucepan, melt the sugar over medium heat until it turns a deep amber. Add the butter and stir until combined, then pour in the warm heavy cream and cook for about 1 minute over low heat, stirring constantly. Let the caramel cool completely.
Once the sponge is baked, let it cool completely. Trim off the domed top and set it aside, then cut the remaining cake horizontally into 3 even layers.
Place a little cream on a serving plate to hold the cake in place, then add the first layer of sponge. Spread a layer of white cream on top, sprinkle with peanuts, then drizzle or spread some caramel over the peanuts. Add the second layer of sponge and repeat the same process.
For the third layer of sponge, use a piping bag fitted with a star or round tip to pipe decorative swirls or any design you like with the remaining cream. Scatter a few peanuts on top, then drizzle a little caramel over the top using a piping bag with a small opening.
hill the cake in the refrigerator for 5–6 hours before slicing and serving.