Make the Cake: Preheat oven to 350F. Butter two 9-inch round cake pans. Line bottoms of pans with parchment; butter parchment. Dust pans with cocoa, tapping out any excess. In a large saucepan over medium heat, bring stout and butter to a simmer. Remove from heat; whisk in cocoa until smooth. Let cool completely.
In a large bowl, whisk together sugar, flour, baking soda, and salt. With an electric mixer, beat eggs and sour cream until combined. Add stout mixture and beat on low speed until combined; add flour mixture and beat until combined. Divide batter evenly between prepared pans smoothing tops with an offset spatula.
Bake until tops spring back when lightly touched and a cake tester comes out with just a few crumbs attached, 35-45 minutes. Transfer pans to a wire rack to cool 10 minutes. Turn out cakes onto rack to cool completely.
Make the Candied Pecans: Line a rimmed baking sheet with a non-stick baking mat. In a small saucepan, heat sugar and 1/4 cup water over medium-high; cook, swirling occasionally, until sugar is dissolved and mixture is medium amber in color, 2 to 3 minutes. Remove from heat; immediately stir in pecans. Pour onto prepared sheet to cool completely. Transfer pecans to a cutting board and coarsely chop.
Make the Salted Caramel: In a small saucepan, heat cream over low. In a medium saucepan, stir together sugar, corn syrup, and 1/3 cup water; cook over medium-high, without stirring, until mixture is dark amber in color, about 15 minutes. Remove from heat; carefully pour in cream (mixture may splatter) and stir until smooth. Reduce heat to medium and cook until a candy thermometer reads 238 F (soft ball stage), about 2 minutes. Pour mixture into a medium bowl; stir in salt. Let cool about 15 minutes, then stir in butter, 1 tablespoon at a time. Let cool completely.
Make the Caramel Buttercream: In a heatproof bowl, whisk together sugar and egg whites. Set over (not in) a pot of simmering water and whisk until sugar is dissolved and a thermometer registers 140 F. Remove bowl from heat. With an electric mixer on medium-high, whisk buttercream mixture until stiff, glossy peaks form. Reduce speed to medium-low and add butter, a few tablespoons at a time; continue beating until smooth. Stir in vanilla and caramel.
Make the Chocolate Ganache: Place chocolate in a medium bowl. In a small saucepan over medium, bring cream just to a boil. Pour over chocolate and let stand 1 minute. Stir until smooth and shiny, then stir in butter. Let cool 20 minutes.
For assembly: With a serrated knife, trim tops of cake layers to level; split each cake in half horizontally to form a total of four layers. Place a layer, bottom-side down, on a cake stand. Spread evenly with about 2 cups caramel buttercream. , then sprinkle with some candied pecans. Drizzle with caramel and sprinkle with a few more candied pecans. Repeat process with remaining cake layers, leaving top layer (bottom-side up) uncovered. For stability, insert a dowel into center of cake, trimmed so that it’s just shorter than the top of cake. Spread ganache over top and sprinkle with remaining candied pecans. Refrigerate 20 minutes before serving.