Add the squash, salt, and water to a covered medium saucepan and bring to a boil. Reduce to a simmer and cook until the squash is fork tender, about 10 minutes. Strain and rinse with cool water, strain again, and reserve.
In a large mixing bowl, combine the cold whipping cream, confectioners' sugar, and vanilla extract. Whisk until soft peaks form. Reserve the whipped cream in the refrigerator.
In a large mixing bowl, combine the cooked squash, sugar, pecans, bourbon, ground cinnamon and nutmeg.
Place 4 small cast-iron bakers on oven burners over medium heat. Evenly divide the butter, cinnamon sticks and squash mixture among the pans. Cook for 5 minutes.
Serve in the cooking pans with vanilla bean ice cream and a dollop of the reserved whipped cream on top.