Butter and flour an 8-inch springform pan. Line bottom of the pan with parchment paper. Put the pan on a baking sheet lined with parchment paper.
To make the cake: Whisk the flour, baking soda and salt together. Melt chocolate and butter together using a double boiler.
In a large bowl whisk the eggs and sugars together until well blended. Whisk in the corn syrup, followed by the vanilla. Whisk in the melted butter and chocolate. Still working with a whisk, gently stir in the dry ingredients, mixing only until they are incorporated. You will have a thick, smooth, shiny batter. Pour the batter into the pan and jiggle the pan a bit to even out the batter.
Bake the cake at 350F for 40-45 minutes, or until a knife inserted into the center comes out almost clean. Transfer the pan to a rack and cool the cake for 15 minutes, then run a knife between the cake and the pan and remove the sides of the pan. During baking, the cake probably will have puffed to the top of the pan don’t be concerned if it sinks a little or it if develops a crater in the center. Cool the cake to room temperature.
When the cake is completely cool, invert it, remove the base of the pan and peel off the paper. Wash and dry the springform pan, and return the cake to it right side up. Refasten the sides around the cake.
To make the topping:
Put the sugar, water and corn syrup in a medium heavy-bottomed saucepan, stir just to combine the ingredients and then put the pan over medium-high heat. Heat, without stirring, until the caramel turns deep amber., 5-10 minutes. Lower the heat a bit and, standing back from the saucepan add the cream and butter. When the spatters are less vehement, stir to calm down the caramel and dissolve any lumps. Stir in the peanuts, and pour the caramel and peanuts into a 1-quart Pyrex measuring cup or heatproof bowl.
Spoon the peanuts on top of the cake. Then spoon the caramel on top of those. You will have extra caramel leftover to use on something else…like ice cream! You’ll have a layer about a ¼ inch high. Allow the topping to set to room temperature about 20 minutes before serving.
To serve, run a blunt knife between the caramel and the pan and simply remove the sides of the springform. If this isn’t the case, hit the sides with some hot air from a hairdryer or wrap the sides in a towel moistened with hot water.