Preheat the oven to 375º F (180º C). Line two round cake pan of about 9 inches (23 cm) with parchment paper.
In a medium size bowl sift together the flour, baking powder and salt.
In a big bowl, beat together the eggs and sugar using an electric mixer or hand whisk for 7 minutes until the mixture turns lighter in color and triples its size.
Add in the flour mixture in three separate additions. Beat for 30 seconds tops after each addition, just until you no longer see the flour. Do not overmix.
In a heat ressistant bowl place the butter and milk and microwave for 2 minutes for the butter to melt and the milk to heat up. Once ready, add in the vanilla extract and oil. You can also do this on the stove using a pot, but it is important not to let the mixture boil.
Add in about 1 C of the previous egg and flour mixture to the butter one and beat until it is well combined. This is to temepr both mixtures.
Carefully pour the butter mixture into the big egg batter bowl and beat for no longer than 1 minutes until you get a soft and smooth batter.
Divide the batter pouring it into both cake pans and making sure you make the big air bubbles come out of each by hitting the cake pans with the batter inside against the kitchen countertop a few times. Bake for 30 minutes until the cakes turn slightly golden brown and a wooden stick comes out clean when inserted.
Once ready, take the cakes out of the oven and let the cakes cool down in the pans for 10 minutes. Then, turn them out and let them completely cool down on a cooling rack.
For the caramel:
Put all the ingredients but the vanilla in a pot, then put it on the stove over low medium heat.
Slowly cook until it boils, stiring constantly with a rubber spatula until it boils. At first a lot of bubbles will form, but they witll not form as much when keeping on cooking and the sugar caramelizes.
Once the caramel has a light brown color take off the heat. This can take up to 20 to 40 minutes depending on your stove. If you have a kitchen termometer, then use it and make sure the caramel reaches 233º F (112º C) before removing it from the heat.
Once cooked, add in the vanilla extract and combine. Let it cool down for at least 15 minutes.
Put the caramel in a bowl and beat with an electric mixer or hand whisk for 3 minutes for it to have a spreadable texture. Set aside until needed.
For the frosting and to assemble:
On a big bowl pu the cream cheese and powdered or confectioners sugar and mix using a hand whisk or an electric mixer for 3 minutes unitl the mixture turns lighter in color and fluffier.
Add in salt and beat for 2 minutes more until you get a soft mixture with a creamy consitency, perfect for decorating a cake.
Place one of the cakes on top of a cake stand or plate where you are going to serve it. Spread about half of the frosting and 1/4 C of the caramel on top, without covering the sides, to make a naked cake.
Place the other cake on top and decorate the cake with the rest of the frosting only on top. Add 1/4 C more of the caramel and decorate as you prefer. Refrigerate the cake for at least 30 minutes before cutting and serving.