Preheat the oven to 350 degrees and lightly grease a small baking dish.

Place the bread cubes in a large mixing bowl. In a separate bowl, whisk together the pumpkin puree, milk, eggs, granulated sugar, pumpkin pie spice, and 1 teaspoon of the vanilla extract until smooth.

Pour the pumpkin mixture over the bread cubes and stir gently until all pieces are coated. Let the mixture sit for 5 minutes so the bread absorbs the liquid.

Transfer everything to the prepared baking dish and spread it into an even layer. Bake for 35 to 40 minutes until the center is set and the top is lightly browned.

While the bread pudding bakes, make the sauce. Melt the butter in a small saucepan over medium heat. Stir in the brown sugar and heavy cream, then bring to a gentle simmer. Cook for 2 minutes, stirring often, until the sauce thickens slightly. Remove from heat and stir in the remaining teaspoon of vanilla extract.

Let the bread pudding cool for 10 minutes before serving. Spoon the warm vanilla sauce over each portion.