Preheat the oven to 350 degrees F and line a 9 by 9-inch pan with parchment paper.
Place the butter and powdered sugar in a large mixing bowl and beat on medium-high speed for 3 to 5 minutes, or until very pale and fluffy.
Stir in the vanilla extract until incorporated.
Add the flour and salt, and stir on medium speed just until smooth.
Press the dough into the bottom of the prepared pan, in an even layer.
Bake for 22 to 28 minutes, or until just beginning to turn golden around the edges.
Make the caramel:*
In a small pot, gently heat the cream, butter, and salt until the butter has melted and the salt has completely dissolved. Remove from heat and add the vanilla.
Place the sugar, corn syrup, and water in a medium pot and cook over medium-high heat, swirling the pot occasionally to distribute the heat evenly. Boil the sugar mixture until the bubbles begin to get smaller and it becomes amber-colored, then reduce the heat to low and pour in the warm cream mixture. Whisk constantly to avoid lumps or crystals, and continue to cook until a candy thermometer registers 240 degrees F.
Immediately transfer the hot mixture to a heat-safe vessel, cool until slightly thickened, and pour the warm caramel over the shortbread. Allow to cool before layering with peanut butter chocolate chip cookie dough.
Make the peanut butter chocolate chip cookie dough:
Place the butter and brown sugar in a large mixing bowl, and beat on medium-high speed for 3 to 5 minutes, or until very pale and fluffy.
Stir in the peanut butter until smooth.
Scrape the bottom and sides of the bowl with a silicone spatula, then stir in the flour until smooth.
Mix in the vanilla and salt, then spread the mixture over the caramel and top with ganache.
Make the ganache:
Place the chopped chocolate in a medium mixing bowl.
Heat the cream in a small pot until just barely simmering, then pour it over the chocolate and let stand for about 3 minutes.
Stir the ganache gently with a silicone spatula, until smooth.
Pour the ganache over the edible cookie dough in an even layer.
Allow to cool until set, then run a thin knife around the edges and remove from the pan.