Preheat your oven to 325°F. Place six ramekins in a baking dish.
Combine the coconut milk, granulated sugar, cornstarch, and salt in a medium saucepan. Whisk over medium heat until thickened, about 5-7.
In a separate bowl, whisk together the egg yolks and a bit of sugar until smooth and slightly pale.
Gradually pour the hot coconut mixture into the egg yolks, whisking constantly. Stir in the vanilla extract and dairy-free milk.
Strain the mixture through a fine-mesh sieve into a clean bowl.
Pour the strained mixture evenly into the prepared ramekins, filling each to about three-quarters full.
Pour hot water into the baking dish around the ramekins, halfway up the sides. Bake for 30-35.
Let the ramekins cool to room temperature, then refrigerate for at least 120.
Before serving, sprinkle brown sugar on top of each crème brûlée and caramelize using a kitchen torch or broil for 1-2.