Preheat your oven to 325°F (160°C). Place four ramekins in a baking dish.
In a medium saucepan, heat the heavy cream and vanilla extract over medium heat until it just begins to simmer. Remove from heat and let it cool slightly.
In a mixing bowl, whisk together the egg yolks and granulated sugar until the mixture is pale and slightly thickened.
Gradually pour the warm cream into the egg mixture, whisking constantly to prevent the eggs from scrambling.
Strain the mixture through a fine-mesh sieve into a large measuring cup or bowl to remove any cooked egg bits.
Pour the custard evenly into the prepared ramekins.
Carefully fill the baking dish with hot water until it reaches halfway up the sides of the ramekins.
Bake in the preheated oven for 30-35 minutes, or until the edges are set but the centers still jiggle slightly.
Remove the ramekins from the water bath and let them cool to room temperature. Cover and refrigerate for at least 2 hours, or overnight.
Before serving, sprinkle a thin layer of brown sugar over each custard. Using a kitchen torch, carefully caramelize the sugar until it forms a crispy, golden crust. If you don’t have a torch, place the ramekins under the broiler for 1-2 minutes, watching closely to prevent burning.