Preheat the oven to 350º F/ 180º C. Line two 7 inch/ 18 cm baking pans with circles of parchment paper. Grease well all around inside the pans.
In a large mixing bowl whisk together the eggs with the sugar until well combined: about 1-2 minutes.
Add the vanilla and the oil and whisk again until smooth.
Combine the yogurt with the baking soda. Mix well until it starts bubbling. Add the mixture to the batter and whisk to combine.
Gradually add the flour and the cocoa powder, mixing gently with a rubber spatula until absorbed.
At the end add also the chocolate chips (if using).
Divide the batter between the prepared pans. Optionally wrap each pan with a sheet of aluminium foil, filled with wet kitchen paper inside (see notes). This will help avoid uneven layers.
Bake the cakes for about 40-50 minutes or until a toothpick inserted in the centre comes out clean.
Let the layers cool completely before assembling the cake.
Frosting:
In a large mixing bowl whip the cream cheese, sour cream and powdered sugar until fluffy.
Melt the chocolate on a double boiler. Mix it gently until it cools down: it shouldn’t be hot when added to the frosting.
Add a small dollop of the whipped frosting to the chocolate using a rubber spatula. Mix very well quickly to combine. Repeat the process 2-3 more times. This is done to “temper” the chocolate so it doesn’t harden fast in the colder frosting.
Transfer the chocolate mixture to the remaining white frosting. Beat with the mixer at a high speed until fluffy and uniform.
Salted caramel sauce:
Place the sugar in a saucepan over medium heat. Whisk continuously until the sugar caramelizes and becomes amber (5-7 minutes).
Add the butter very carefully as it will start splashing (wear kitchen gloves). Whisk continuously until the butter combines with the sugar into a sticky mass.
When the butter and sugar are combined, slowly and carefully pour the cream. Whisk for a few seconds, until the mixture becomes uniform.
Remove the pan from the heat and add the salt. Whisk again.
Let the caramel cool completely before using it in the cake. Store the leftovers in the fridge.
To assemble:
Using a long serrated knife cut the cooled layers horizontally into two parts each.
Place one layer on a serving plate. Generously spread frosting on top. Spoon 2 tablespoon salted caramel over the frosting.
Repeat the process until using all layers. You should have enough frosting left to spread all around the cake.
Pour the remaining caramel sauce on top. Use a spoon to make drips around the cake.
Decorate with chopped nuts, chopped chocolate or sprinkles.
Ideally serve the cake after it stays 3-4 hours in the fridge.
Notes
You can use any type of granulated sugar for the layers but I recommend the dark brown for its caramel taste. Use only granulated cane sugar for the caramel!
For the frosting you can use milk or dark chocolate but avoid over 60% cocoa content as it will make the frosting too thick.
To bake even layers, wrap the outside of each cake pan with aluminium foil with wet paper towel wrapped inside it. To make this, wet pieces of kitchen paper, place them into long sheets of aluminium foil and wrap the foil around the paper to create sheets as wide as the pan sides. Then wrap the sheets of foil with the paper inside tightly around the cake pans.
Remove the cream cheese and sour cream from the fridge about 30 minutes before making the frosting. This will help avoid lumps in the frosting.
For a move evenly assembled layers you can use a cake ring. Remove it before frosting the cake around.
Keep the leftovers covered in the fridge for 3-4 days. You can freeze the cake in airtight containers for up to 2 months.