Special equipment: 2 round 8-inch baking pans for 1 large cake or 6 small baking pans for 3 smaller cakes
Preheat the oven to 350 degrees F.
In a large bowl, combine the flour, baking powder, and salt. Stir to blend. In the bowl of an electric mixer fitted with the whisk attachment, beat the butter until smooth and add the sugar. Continue whipping until the mixture becomes fluffy, 2 to 3 minutes. Note: this process can be done with a whisk by hand. Add the eggs, 1 at a time, taking care that each egg is thoroughly integrated. Add the flour mixture and combine. Add the lemon zest and lemon juice and whisk to blend.
Grease the 2 pans with butter and fill each with half of the batter. Place the pans in the center of the oven. Bake until the center is firm or when the tip of a small knife emerges clean when it pierces the center of each cake, 30 to 40 minutes. Remove from the oven and allow to cool thoroughly, 1 hour at least. Once completely cool, using a serrated knife, slice each cake in half horizontally to form 4 equal layers. Place the layers on a flat surface. Set aside.
In a medium bowl, combine the chocolate and sugar. In a medium pot over low heat, combine the heavy cream and vanilla and bring to a simmer. Pour over the chocolate and stir until all of the chocolate has melted. Gently whisk in the butter pieces. Set aside to cool.
When the frosting is cool, whip the frosting in the bowl of a mixer fitted with a whisk attachment. Whip to lighten the frosting, 1 to 2 minutes. Frost each layer of the cake, stacking them neatly and uniformly on top of each other. Then frost the entire outside of the cake as well.
In a medium skillet, heat the sugar until it "melts" and turns a caramel color. Stir in the butter. Pour the caramel directly over the top of the cake, allowing it to drip down the sides to create a caramel shell. Allow the caramel topping to cool and harden on top of the cake.
Recipe courtesy of Alex Guarnaschelli