Salted-Caramel Six-Layer Chocolate Cake

• Unsalted butter, room temperature, for pans
• 3 cups all-purpose flour, plus more for pans
• 3 cups granulated sugar
• 1 1/2 cups unsweetened Dutch-process cocoa powder
• 1 tablepoon baking soda
• 1 1/2 teaspoons baking powder
• Coarse salt
• 4 large eggs
• 1 1/2 cups low-fat buttermilk
• 1/2 cup plus 2 tablespoons safflower oil
• 2 teaspoons pure vanilla extract

For the Caramel

• 4 cups granulated sugar
• 1/4 cup light corn syrup
• 2 cups heavy cream
• Coarse salt
• 2 sticks cold unsalted butter, cut into tablespoons

For the Frosting

• 1/4 cup plus 2 tablespoons Dutch-process cocoa powder
• 2 sticks unsalted butter, room temperature
• 1/2 cup confectioners’ sugar
• Coarse salt
• 1 pound semisweet chocolate, chopped, melted, and cooled
• Garnish: flaked sea salt, such as Maldon