Combine the heavy cream, vanilla, and persimmons in a medium saucepan. Heat over medium heat until the cream just begins to simmer. Do not boil.
Remove from the heat and let cool for about 15 minutes. Transfer the mixture to a blender or food processor and blend until completely smooth.
Preheat the oven to 300°F. Arrange four 6-ounce ramekins in a roasting pan or deep baking dish.
In a medium bowl, whisk the egg yolks, 3 tablespoons sugar, and salt until smooth.
Slowly pour the warm persimmon cream into the egg yolks while whisking constantly.
For an extra-smooth custard, pour the mixture through a fine-mesh strainer into a measuring cup or bowl.
Divide the custard evenly among the ramekins.
Place the roasting pan on the middle oven rack. Carefully pour hot water into the pan until it reaches about halfway up the sides of the ramekins.
Bake for 35–40 minutes, or until the edges are set but the centers still have a slight jiggle.
Carefully remove the ramekins from the water bath and let cool to room temperature. Cover and refrigerate for at least 2 hours or up to 2 days.
Just before serving, sprinkle about 1 teaspoon sugar evenly over each custard.
Using a kitchen torch, caramelize the sugar until bubbling and deep golden brown. Let stand for 1–2 minutes, until the sugar hardens into a crisp shell.