Preheat oven to 350F degrees. Scatter the torn croissants evenly in a single layer on a baking sheet. Bake until dry and toasted, about 10-12 minutes. Allow croissants to cool while you prepare the custard.
Begin by making the Salted Caramel: In a medium saucepan over medium heat, combine the sugar and water and gently swirl (NOT stir) the pan around occasionally as it begins to boil. Continue boiling until the caramel reaches a golden brown, about 5 to 10 minutes.
Remove pan from the heat and carefully whisk in the heavy cream. Caramel will sizzle and bubble up. Stir in the salt, and continue whisking until caramel is smooth. If needed, return pan over medium-low heat until caramel is smooth. Transfer to dish or glass measuring cup to cool. Caramel will continue to thicken as it cools.*
In a medium bowl, whisk together the milk, egg yolks, egg, brown sugar, and vanilla. Pour 1 and 1/4 cups of the slightly cooled salted caramel into the custard and whisk until combined.
Transfer cooled croissants to an 8-inch square baking dish. Pour custard over croissants, let stand, occasionally pressing down on the croissants until fully saturated, about 40-50 minutes.
Sprinkle granulated sugar evenly over bread pudding. Bake in the oven for 35-40 minutes, or until the custard has just set. Remove from the oven and allow to cool for 20 minutes.
Serve with reserved salted caramel sauce.