Place the bread slices into a shallow baking dish, in one single layer. Pour the cream mixture over the bread, completely immersing the bread in the liquid.
Melt the butter in a large frying pan over medium heat. When the butter melts, fry 4 to 5 slices at a time until golden brown, 3 to 4 minutes per side. Using a spatula, transfer the French toast to a cooling rack. Repeat for the remaining bread, adding additional butter to the pan as necessary. Reserve the remaining cream mixture for a later use.
As the French toast cools, generously butter a 9-inch springform pan.
Preheat the oven to 350 degrees F and position a rack in the center of the oven.
To build the cake, create a complete layer of French toast in the springform pan, pressing the pieces against each other to fill the space. You might need to trim pieces to fit exactly into the pan.
For the filling: Mix the peanut butter with the sugar. Scatter 4 to 5 teaspoon-size pieces of sweetened peanut butter and caramel candy over the layer of French toast. Repeat with two more layers of French toast and the remaining peanut butter and candy pieces, then sprinkle on the fleur de sel.
Place the pan on a lined baking sheet. Using a fork, punch some holes over the surface of the cake, then pour in the reserved French toast soaking liquid.
Bake until the cake swells like a souffle and is golden, 35 minutes.
Remove the cake from the oven and cool completely on a wire rack, approximately 2 hours. Refrigerate until the cake is cold, an additional hour. While the cake is chilling, prepare the chocolate glaze.
For the glaze: Pour the chocolate, butter and corn syrup into the top of a double boiler and melt over medium-low heat. Stir the ingredients until the chocolate and butter melt and the glaze appears shiny, about 5 minutes.
Pour the glaze into a 1-pint measuring cup or a small pitcher with a spout.
Using a candy thermometer, monitor the temperature, let cool to 90 to 95 degrees F before using.
To finish the cake, run a sharp knife along edge of the cake to remove it from the pan. Unlock and remove the springform pan. Place a baking rack on the top of the cake and invert the cake onto the rack. Using an offset spatula, remove the bottom of the cake pan.
Place the baking rack with the cake onto a baking sheet to catch the glaze drippings. Pour the glaze over the cake. Pick up the baking rack and strongly bang it against the baking pan to even out the glaze. Run a hot offset spatula along the bottom of the cake to release it from the rack and hold the cake with one hand centered underneath the cake. Using your opposite hand, carefully press the chopped peanuts evenly on the sides of the cake.
Place the cake on a serving platter and refrigerate until the glaze is firm, about 10 minutes.
Store, lightly covered, in the refrigerator for up to 3 days.