Preheat the oven to 350 degrees and lightly grease a baking dish.
In a large bowl, whisk together the pumpkin puree, milk, eggs, brown sugar, pumpkin pie spice, and vanilla extract until smooth.
Add the cubed bread to the bowl and stir gently until every piece is coated. Let the mixture sit for five minutes so the bread can absorb the liquid.
Pour the mixture into the prepared baking dish and drizzle the melted butter over the top.
Bake for 35 to 40 minutes until the center is set and the top turns golden.
While the bread pudding bakes, stir together the maple syrup, powdered sugar, and milk in a small bowl to form the glaze.
Remove the dish from the oven and let it cool for five minutes. Drizzle the maple glaze evenly over the surface before serving.