Step 1In a Dutch oven, small pot or heatproof saucepan, add the sugar. Set the pan on a grill or stove-top burner over medium heat.
Step 2Using a heatproof spatula, push the sugar into a mound towards the back of the pot. As the sugar melts, you will see the edge transform into a golden brown liquid. Gently incorporate small amounts of sugar into the liquid and continue moving the growing pool of caramel. If the caramel begins to smoke, immediately remove it from the heat and return to heat when the smoke subsides.
Step 3When you have integrated about 3/4 of the sugar into caramel, pour the cream and corn syrup into a small saucepan and set over a low flame.
Step 4Keep an eye on the heating cream. Slowly raise the heat to medium as the caramel process is almost complete. You want the caramel to be a liquid amber just as the cream begins to boil.
Step 5Turn off both flames and slowly pour the cream into the caramel. Be very careful — the caramel will bubble up aggressively and the steam will be very hot. When the boil reduces a bit, stir in 1 tablespoon of chilled butter at a time. Stir in the fleur de sel and pour the caramel into a heatproof vessel. This makes about 3 cups caramel. Cool to room temperature, then refrigerate until needed. Warm before serving.
Step 1In a medium saucepan set over a grill or stove-top burner over medium heat, combine the heavy cream, milk and vanilla extract and bring to a boil.
Step 2Meanwhile, in a large bowl, whisk together the eggs and sugar.
Step 3When the cream comes to a boil, transfer the hot cream to a heatproof container with a spout.
Step 4Whisking the eggs with one hand, slowly stream the hot cream into the egg mixture, creating a smooth custard base. Set aside to cool to room temperature.
Step 5Place the cubed bread into an extra large mixing bowl. Pour the custard over the bread. Gently squeeze the brioche cubes until they are uniformly saturated with custard.
Step 6Generously butter a 2- to 2 ½ quart cast iron or other bundt pan or dutch oven, and drizzle about 1 cup of liquid caramel on the bottom. Fill with the bread pudding, making sure there are no air pockets as you go.
Step 7Bake in a covered grill or in a 350-degree oven until the bread pudding puffs up like a soufflé with a golden crown, 30 to 40 minutes. Finish with more liquid caramel and a sprinkle of fleur de sel.
Step 8Set aside to cool for 10 minutes, then top with softly whipped cream to serve.