Slice focaccia horizontally into three even layers. Using an offset spatula, spread artichoke-lemon pesto evenly over bottom layer. Top with peppers and three tablespoons basil pesto. Cover with middle bread layer; spread with an even layer of tapenade. Top with prosciutto, basil, and final bread layer.
In the bowl of an electric mixer fitted with the paddle attachment, beat mascarpone and remaining basil pesto until smooth. Season with salt and pepper.
Using an offset spatula, spread mascarpone cheese mixture evenly over cake. Transfer to a serving platter. Place in refrigerator until very firm, at least one hour or overnight. Remove from refrigerator; garnish with prosciutto, tomatoes, artichoke hearts, olives, and basil.
Using store-bought ingredients makes this cake a cinch to prepare. The pestos, tapenade, peppers, and artichokes can be found at a local gourmet food shop or in the prepared-foods section of your supermarket. You may substitute more basil pesto for the artichoke-lemon pesto, if desired.