Preheat the oven to 375 degrees F. Cut the brioche into four 2-inch-thick slices and arrange in a single layer in a 9-by-13-inch baking dish.
Whisk together the maple syrup, vanilla, salt, whole eggs and yolks and 3 cups of the milk in a medium bowl. Pour the mixture over the bread. Let soak, refrigerated, for 15 minutes. Flip the slices over and let soak, refrigerated, until almost of all the mixture has soaked into the bread, about 15 minutes more.
Line a baking sheet with parchment and spray with cooking spray. Transfer the bread to the prepared baking sheet, letting as much of the milk mixture drip off before transferring as possible. Bake until light golden brown on top and the custard is completely cooked through, about 35 minutes. Transfer to a heatproof serving platter.
Meanwhile, combine the brown sugar, butter and cinnamon in a medium saucepan over medium-high heat and cook, whisking occasionally, until melted and smooth, about 3 minutes. Pour in the remaining 2 tablespoons milk and bring to a simmer. Cook, whisking frequently, until the sugar is dissolved and the sauce is thickened, about 5 minutes. Set aside.
Sprinkle the top of each slice of bread with 2 tablespoons of the granulated sugar. Use a kitchen blowtorch to melt the sugar and caramelize it. Let sit for 5 minutes until hardened. Serve warm with the caramel syrup on the side.
Propane gas torches are highly flammable and should be kept away from heat, open flame and prolonged exposure to sunlight. They should be used only in well-ventilated areas. Follow torch manufacturer's instructions for use.
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