Preheat the oven to 400 degrees F. Line a sheet pan with aluminum foil.
Cut the pumpkin in half and scoop out the seeds and membranes. Place the pumpkin cut side down on the prepared sheet pan. Roast for 30 to 40 minutes until the pumpkin is very tender and soft. Let the pumpkin cool slightly before using a spoon to remove the flesh. Puree in a food processor or blender. Reserve 3/4 cup pumpkin puree for the ice cream. Save the remaining puree for another use.
In a small bowl, mix together 1 tablespoon milk and the cornstarch.
In a large bowl, whisk together the cream cheese and salt. Add the honey and pumpkin puree stirring until fully combined.
In a large saucepan over medium high heat, combine the remaining milk, heavy cream, brown sugar, corn syrup and 5-spice powder. Bring the mixture to a rolling boil and boil for 4 minutes. Remove from the heat and whisk in the milk-cornstarch mixture. Return to a boil for 1 minute.
Slowly pour the hot milk mixture into the large bowl with the pumpkin and whisk to combine.
Cool over an ice bath. Refrigerate until chilled completely.
Churn in an ice cream maker following the manufacturer’s instructions. Freeze the ice cream in an airtight container to allow it to harden before serving.