Preheat the oven to 350°F and line the bottom of a 9-inch springform pan with parchment paper. Separate the egg yolks from the egg whites and set the egg whites aside. Mix the egg yolks with the vegetable oil, vanilla extract, and 1 tbsp of sugar.
In a separate bowl, combine the egg whites, 3 tbsp of sugar, and pinch of salt into a fluffy cream. Add the flour, corn starch, and egg mixture from Step #1, and stir until smooth. Pour the batter into the pan and bake for 15 minutes.
Once the cake has cooled, flip the cake over onto a plate or platter, and put the removable springform pan ring back around the cake, without the base.
Mix the mascarpone, powdered sugar, and whipped cream together, and pour about ⅓ of the cream over the cake.
Dip the ladyfingers in cooled milk coffee, evenly distribute them over the cream, and cover the ladyfingers with another layer of cream. Repeat the process until the pan is full, and the top layer is cream. Refrigerate for at least 4 hours.
Remove the springform pan ring and sprinkle coffee grounds and cocoa powder over the top of the cake before serving.