Preheat the oven to 350˚. Brush the bottom and sides of two 8-inch round cake pans with vegetable oil and dust with flour, tapping out the excess. Whisk the flour, cocoa powder, salt, baking powder and baking soda in a medium bowl. Whisk the vegetable oil, buttermilk and vanilla in a large liquid measuring cup.
Beat the granulated sugar and eggs in a large bowl with a mixer on medium speed until combined. Increase the speed to medium high and beat until very fluffy and light, 4 to 5 minutes. Reduce the speed to medium and beat in the flour mixture in three batches, alternating with the buttermilk mixture, until combined, stopping to scrape down the bowl occasionally. Divide the batter evenly between the prepared pans.
Bake until the tops of the cakes are firm and spring back when gently pressed and the sides begin to pull away from the pan, about 45 minutes. Transfer to a rack and let cool 15 minutes, then run a thin spatula around the cakes to loosen and invert onto the rack to cool completely.
Meanwhile, make the frosting: Beat the butter, cream cheese, vanilla and salt in a large bowl with a mixer on medium-high speed until light and fluffy, 3 to 5 minutes. Beat in the dulce de leche until well combined. Reduce the mixer speed to low and beat in the confectioners' sugar until combined, then increase the speed to medium high and beat until the frosting is thick and fluffy, about 1 more minute. Refrigerate until the frosting is slightly firm but still spreadable, about 1 hour.
Trim the domed tops of the cakes with a long serrated knife to make them level, if necessary. Cut each layer in half horizontally to make 4 thin layers. Put 1 layer on a cake plate and spread with a heaping 1/2 cup frosting all the way to the edges. Repeat with 2 more cake layers, then top with the remaining cake layer. Cover the top and sides of the cake with a thin layer of frosting (this is the crumb coat—it doesn’t have to be perfect). Refrigerate until set, about 1 hour. Reserve the remaining frosting.
Mix the cocoa powder and hot water in a small bowl until smooth. Add 1/2 cup of the remaining frosting and stir well to combine. Refrigerate the chocolate frosting and remaining dulce de leche frosting along with the cake.
Cover the cake with the remaining dulce de leche frosting. Using a small offset spatula, add swipes of the chocolate frosting in concentric circles over the top of the cake, plus some swipes around the sides of the cake. Use a large offset spatula to smooth the chocolate frosting into the dulce de leche frosting, slightly marbling the two. Run the tines of a fork around the top of the cake in concentric circles. Refrigerate until set, at least 30 minutes or overnight.
Meanwhile, make the chocolate curls: Run the palm of your hand on one side of the chocolate block to soften slightly. Working over a piece of parchment paper, scrape along the softened side with a paring knife or a wide vegetable peeler to make about 2 cups large chocolate shavings. Freeze on the parchment until set, 10 minutes.
Remove the cake from the refrigerator. If the frosting is too hard, let stand until softened, about 15 minutes. Gently press the chocolate shavings into the sides of the cake.