Preheat oven to 350°F (177°C). Scatter torn croissants on a baking sheet and toast for 8–10 minutes until dry and lightly golden. Toast walnuts in the same oven for 8–10 minutes, then let cool.
In a large bowl, whisk maple syrup, brown sugar, egg yolks, egg, vanilla, cinnamon, and salt until smooth. Add heavy cream and milk; whisk until well combined.
Fold in the croissants until fully saturated in the custard, then gently fold in toasted walnuts.
Pour the mixture into a greased 8-inch square baking dish, pressing down gently to submerge all pieces. Let soak for at least 2 hours (or overnight in the refrigerator).
Preheat oven to 350°F (177°C). Sprinkle 1 tablespoon sugar evenly over the top and bake for 40–45 minutes, until golden and set.
For the brown butter maple sauce: Combine sugar, flour, and salt in a small bowl. Melt butter in a medium saucepan over medium-low heat, stirring until golden brown and nutty. Whisk in the sugar mixture, then slowly add cream. Simmer until thickened, then stir in maple syrup and vanilla.
Serve warm bread pudding drizzled generously with brown butter maple sauce. Garnish with extra walnuts if desired.