Preheat your oven to 350°F (175°C). Grease and flour two 9-inch round cake pans.

In a large bowl, cream together 1/2 cup softened butter, vegetable oil, and granulated sugar until light and fluffy.

Add eggs one at a time, beating well after each addition. Stir in 1 tablespoon vanilla extract.

In a separate bowl, whisk together flour, baking powder, and 1/2 teaspoon salt.

Gradually add dry ingredients to the creamed mixture alternately with milk, starting and ending with the flour mixture.

Divide the batter evenly between the prepared pans.

Bake for 25-30 minutes, or until a toothpick inserted into the center comes out clean.

Cool cakes in the pans for 10 minutes, then turn out onto wire racks to cool completely.

For the caramel frosting, combine brown sugar, 1/2 cup butter, and heavy cream in a saucepan over medium heat. Bring to a boil, stirring constantly, and cook for 1 minute.

Remove from heat and transfer to a mixing bowl. Add 1/4 teaspoon salt and 1 teaspoon vanilla extract.

Gradually beat in powdered sugar until frosting is smooth and reaches spreading consistency.

Frost the cooled cake layers, and stack them. Spread frosting over the top and sides of the cake.