Preheat your oven to 375°F. Grease a small cast iron skillet generously with butter or nonstick spray. Add the cubed brioche bread evenly into the skillet.
In a medium bowl, whisk together the eggs, heavy cream, whole milk, vanilla extract, rum extract, cinnamon, nutmeg, brown sugar, and melted butter until smooth and fully combined.
Pour the custard mixture evenly over the cubed brioche bread, pressing gently so every piece absorbs the liquid. Let it sit for 5 to 10 minutes to fully soak.
Sprinkle with Turbinado sugar
Bake at 375°F for 45 to 50 minutes, or until the center is set and a knife inserted comes out clean. The edges should be crispy, golden brown, and caramelized.
While the bread pudding bakes, prepare the caramel sauce.
In a small saucepan over medium heat, combine the butter, heavy cream, brown sugar, and vanilla extract. Stir continuously until the mixture becomes bubbly and thick, about 5 minutes.
Remove from heat.
Pour the warm caramel sauce generously over the bread pudding. Serve immediately with a scoop of vanilla ice cream on top.
The contrast of warm bread pudding, rich caramel, and melting ice cream creates the perfect restaurant-quality dessert experience at home.