Thinly grease the sides of a 6-inch round cake pan with unsalted butter.
In a small saucepan, combine 66g granulated sugar and 33g water. Heat over medium without stirring until it turns a deep amber color. Remove from heat, carefully stir in 33g hot water to stop cooking. set.
Pour into the cake pan. Place in the refrigerator to set.
Preheat oven to 300°F (150°C). Warm 165g whole milk and 165g heavy cream in a small saucepan over medium-low heat until it reaches 140°F–158°F (60°C–70°C).
In a separate bowl, whisk 3 large eggs and 100g granulated sugar until smooth. Gradually pour the warm dairy into the egg mixture in 2 to 3 additions, whisking constantly.
Place 285g kabocha purée in a large bowl. Whisk in the warm egg-milk mixture in 2 to 3 additions until blended, then stir in 15g dark rum (if using).
Pass the entire mixture through a fine-mesh sieve, pressing the pumpkin solids through with a spatula for a silky texture.
Pour the strained batter into the cake pan over the set caramel. Place the cake pan inside a larger roasting pan and fill the outer pan with hot water (160°F–175°F / 70°C–80°C) until it reaches halfway up the side of the mold.
Bake at 300°F (150°C) for 50 to 60 minutes in a conventional home oven (40 to 45 minutes in a commercial convection oven) until the center is set with a slight, firm jiggle.
Remove from the water bath, cool to room temperature, and refrigerate overnight (at least 8 hours).
To unmold, run a thin spatula around the top inside edge, invert onto a serving plate, and wrap a warm, damp cloth around the pan for 10–15 seconds to release.
Slice with a hot, clean knife and serve with whipped cream and a dusting of cinnamon and nutmeg.