Preheat the oven to 350°F (175°C). Lightly grease two 4-inch round cake pans, line bottoms with parchment paper rounds, and grease the parchment. Set aside on a baking sheet for easier handling in and out of the oven.
In a medium mixing bowl, whisk together the flour, Dutch-process cocoa powder, granulated sugar, baking soda, and fine sea salt until thoroughly blended and no cocoa lumps remain. This ensures even leavening and smooth chocolate flavor in the finished layers.
In a separate small bowl or jug, whisk together buttermilk, oil, egg, and vanilla extract until fully emulsified and smooth. Stream in 60 ml hot water and whisk again, this helps bloom the cocoa and keeps the batter glossy and fluid.
Pour the wet ingredients over the dry mixture. Whisk gently until just combined; scrape bowl and fold with a spatula to ensure no flour pockets remain. Batter should appear shiny, pourable, and free of lumps but do not overmix.
Divide the batter evenly between the prepared pans (about 170g per pan). Smooth tops with a spatula. Bake on the center rack for 22-26 minutes until a cake tester emerges with only moist crumbs, not wet batter. Avoid overbaking.
Remove pans to a wire rack and cool for 10 minutes. Run a thin knife around edges and invert onto racks. Peel off parchment and cool completely. For neat stacking, wrap layers and refrigerate 45-60 minutes until chilled and firm.
In a medium bowl, beat unsalted butter with a hand mixer on medium-high until very pale and fluffy, about 2 minutes. Beat in powdered sugar, scraping once midway, until creamy. Add caramel sauce and 2 tablespoons heavy cream; beat until smooth and spreadable. Add a touch more cream if needed for silky consistency.
Place one cake layer on a serving board. Spread generously with caramel buttercream (about ⅓ of total). Stack the second layer and apply a thin crumb coat over the entire cake. Chill for 20 minutes. Apply remaining buttercream in a smooth, even layer, using an offset spatula to create tall, tidy sides.
In a heatproof bowl, melt the chopped chocolate in 15-second intervals in the microwave, stirring between, until mostly smooth. Stir in caramel sauce and 2 teaspoons heavy cream. Mix until glossy and fluid but thick enough to mound lightly on a spoon. Let cool to just warm, about 95°F (35°C), before decorating.
With the cake chilled, use a spoon or piping bag to gently nudge the glossy drip over the cake edge, allowing it to flow naturally. Cover the top with remaining drip for a domed look. Sprinkle flaky sea salt over the drip once it begins to set but is still slightly tacky to the touch.