Prepare stuffing mix according to box directions to make a drier stuffing. Set aside.
Cook squash until well done. Peel, remove seeds and strings and press out most of the liquid, reserving the liquid. Lightly puree in blender or processor with peeled and skinned chestnuts and butter, adding back just enough of the reserved liquid as necessary to keep the puree at a mayo-to-peanut-butter consistency. Add salt and nutmeg to taste.
Mix the eggs into the stuffing mix until well-blended. Add any remaining reserved liquid from the squash to keep moist. Spread on a standard size cookie sheet lined with parchment to about 1/2" thick. Bake at 350F until the egg is set but it is still flexible. Let cool for a bit.
Spread stuffing sheet with squash and chestnut mixture. very lightly dust with cinnamon. Starting on a short side, start gently loosely rolling up the sheet. Be careful to not pinch too hard as the squash will sqeeze in the direction you are rolling. Use the parchment as an aid to keep the roll straight. As the roll is completed, it should end up on the seam. Leave it on the same pan, but try to get a little non-stick spray underneath on the pan.
Return the roll to the 350F oven and bake until the internal temp reaches 160°F Cool a little then slice on a bias.
Serve placed over sliced turkey or pork and ladle with gravy. Realize chestnut is that flavor you've been trying to place with no luck for the last 27 years.