Freeze the bowl of your ice cream maker at least 24 hours in advance. Place a 8 to 9 inch metal pan in freezer to chill.
Add the Roasted Chestnuts (1 cup) in a saucepan with half of the Milk (8 fluid ounce) bring to a simmer and cook for 10 minutes, add contents to a Vitamix or food processor and blend until perfectly smooth, reserve.
Add Heavy Cream (16 fluid ounce), remaining Milk (8 fluid ounce), 3/4 cup Muscovado Sugar (3/4 cup) Honey (1/2 cup) and Salt (1/4 teaspoon) to a saucepan and cook over medium heat, stirring occasionally until mixture reads 175 degrees F (80 degrees C) about 5 to 10 minutes.
While cream mixture is heating, whisk the Egg (6) and remaining Muscovado Sugar (1/4 cup) in a bowl until smooth, slowly whisk in 1 cup of warm cream mixture into yolk mixture to temper the yolks.
Add tempered yolk mixture to the saucepan and cook over medium low heat until mixture thickens and registers 180 degrees F (82 degrees C), about 7 to 10 minutes.
Stir in chestnut puree and Vanilla Extract (1 tablespoon) until well combined with custard. Strain custard into a bowl through a fine mesh strainer and cool until it is no longer steaming, about 10 to 20 minutes.
Reserve 1 cup of the custard mixture into a small bowl, cover with plastic wrap and place in freezer. Cover large custard bowl with plastic wrap and refrigerate for at least 4 hours or up to 24 hours
Remove custards from refrigerator and freezer and scrape frozen custard into large bowl of custard, stir occasionally until frozen custard has fully dissolved.
Transfer custard to ice cream machine and churn until soft serve registers 21 degrees F (-6 degrees C), for 15 to 25 minutes.
Transfer ice cream to the frozen baking pan and press plastic wrap on surface, return to freezer until firm around the edges for about 1 hour.
Transfer ice cream to an airtight container and freeze until firm, at least 2 more hours.