The Best Caramel Cake

Ingredients

• 2 cups sugar
• 1 cup heavy cream
• 2/3 cup butter (cut into cubes)
• 4 tablespoons water
• 1 1/4 cups all-purpose flour (sifted)
• 1 1/4 cups cake flour (sifted)
• 1 teaspoon salt
• 1/2 teaspoon baking soda
• 2 teaspoons baking powder
• 1/2 cup butter
• 1 1/2 cups sugar
• 1/2 cup vegetable oil
• 3 large eggs
• 2 tablespoons vanilla extract
• 1 1/4 cups milk (undiluted evaporated milk can be used for extra richness)
• 3 1/2 to 4 cups powdered sugar
• 1/2 cup caramel sauce
• 2 teaspoons vanilla extract
• a few tablespoons milk