Tuxedo Cake

Name: Tuxedo Cake
Prep time: 1 h 10 min
Cook time: 28 min
Total time: 1 h 38 min
Cuisine: American
Ingredients: 2 cups granulated sugar; 1 cup unsalted butter (melted and cooled); 1/4 cup vegetable oil; 3 large eggs (at room temperature); 2 teaspoons vanilla extract; 2 1/2 cups all-purpose flour; 2 teaspoons baking powder; 1 teaspoon baking soda; 1/2 teaspoon salt; 1 cup unsweetened cocoa powder; 1 1/2 cups warm coffee (or substitute flat cola); 4 ounces semisweet chocolate (finely chopped); 1/2 cup + 3/4 cup heavy cream (divided and very cold); 1 teaspoon light corn syrup; 2 tablespoons granulated sugar; 4 ounces white chocolate; 4 ounces cream cheese (at room temperature); 2 tablespoons unsalted butter (at room temperature); 1/2 cup powdered sugar; 1/8 teaspoon salt; 1 1/2 cups unsalted butter (at room temperature); 1/2 cup unsweetened cocoa powder; 4 1/2 to 5 1/2 cups powdered sugar; 3 to 4 tablespoons whole milk or heavy cream; 1 teaspoon vanilla extract; 1/2 teaspoon espresso powder (optional); 1/2 cup heavy cream; 4 ounces dark chocolate (finely chopped)