In a large bowl, whisk together the eggs, heavy cream, pumpkin puree, pumpkin spice, ¼ cup of sugar, and 1 teaspoon of vanilla extract. Spread half of this mixture evenly across the bottom of a baking dish.
Slice the Hawaiian rolls lengthwise to create separate top and bottom halves. Place the bottom half in the baking dish and set the top half aside.
In a medium bowl, beat the cream cheese, ½ cup of sugar, and 1 teaspoon of vanilla extract until smooth and creamy. Spread this mixture evenly over the bottom buns, then place the top half of the buns on top of the cream cheese layer.
Pour the remaining egg mixture over the entire casserole.
In a small bowl, combine the melted butter, brown sugar, and pumpkin spice. Sprinkle this mixture generously over the top of the casserole.
Cover the dish with foil and refrigerate for at least 1 hour, or overnight for best results.
When you're ready to bake, preheat the oven to 350 degrees Fahrenheit.
Bake the casserole covered for 35 minutes. Then, remove the cover and bake for an additional 15 to 20 minutes, or until the center is set and no longer jiggles. Allow it to cool slightly before serving.