Step 1: Preheat your oven to 350°F (175°C). Lightly grease an 8x8-inch baking dish. Tear or cut the Hawaiian rolls into bite-sized pieces (about 1-inch cubes) and spread them evenly in the prepared baking dish.
Step 2: In a large mixing bowl, whisk together the half and half, pure pumpkin puree, eggs, and vanilla extract until smooth. Add the granulated sugar, ½ cup light brown sugar, cinnamon, and pumpkin pie spice. Whisk again until all ingredients are well combined and the sugars are dissolved.
Step 3: Pour the pumpkin mixture evenly over the bread cubes in the baking dish. Gently press the bread down to ensure all pieces are submerged and absorb the liquid. Let the mixture sit for at least 15-20 minutes at room temperature, or cover and refrigerate for up to an hour (or overnight) for deeper flavor absorption.
Step 4: Bake uncovered for 35-45 minutes, or until the pudding is set, golden brown on top, and a knife inserted into the center comes out mostly clean (a little moistness is good!).
Step 5: While the bread pudding bakes or cools slightly, prepare the brown sugar sauce. In a small saucepan over medium heat, melt the butter. Add the remaining 1 cup of packed light brown sugar. Stir constantly until the sugar has dissolved and the mixture is smooth and bubbly, about 2-3 minutes.
Step 6: Carefully pour in the heavy cream, stirring vigorously. Continue to cook and stir for another 2-3 minutes, allowing the sauce to thicken slightly. Remove from heat and let it cool for a few minutes; it will thicken further as it cools.
Step 7: Once the pumpkin bread pudding is out of the oven, let it cool for a few minutes. Drizzle generously with the warm brown sugar sauce. Serve immediately with a scoop of vanilla ice cream or a dollop of whipped cream for an extra special treat.