Heat a fire to medium-high heat or heat the oven to 400 degrees F.
Rinse the chestnuts under cold water and pat them dry. Use a paring knife to score an x in the bottom of each chestnut. Scoring the chestnuts allows the steam to escape so they don't explode with the heat of the fire or oven.
Place the chestnuts on a sheet tray (if roasting in the oven) or in a roasting pan (if roasting on a fire). Roast the chestnuts for 20 to 30 minutes, shaking them gently every once in a while to keep them from browning too much in any one spot. Set aside and allow to cool for a few minutes.
Meanwhile, add the cream to a large bowl and beat with an electric hand mixer until it looks thick, like melted ice cream. Sprinkle in the sugar and add the vanilla bean seeds and continue to whip until soft peaks appear. Place in a serving bowl and serve alongside the chestnuts.