Preheat your oven to 325°F. For the caramel, combine 1/3 cup allulose and water in a small saucepan over medium heat. Stir until the allulose dissolves, then stop stirring and let it cook for 5 to 8 minutes until it turns a deep amber color.
Immediately pour the caramel into a 9-inch round cake pan, quickly tilting to coat the bottom evenly. Set aside to harden. In a large bowl, gently whisk together the eggs and egg yolks until combined - do not whip or create foam. You want a smooth custard, not an airy one.
In a saucepan, warm the coconut milk, heavy cream, and 1/2 cup allulose over medium heat, stirring until the allulose dissolves. Remove from heat and stir in the vanilla extract and salt.
Very slowly pour the warm milk mixture into the eggs in a thin stream, whisking gently the entire time. Strain the custard through a fine mesh sieve into the caramel-lined pan to ensure a perfectly smooth texture.
Place the cake pan inside a larger baking dish and pour hot water into the larger dish until it comes halfway up the sides of the cake pan. Cover the top loosely with aluminum foil.
Bake for 50 to 60 minutes until the flan is set around the edges but still has a gentle wobble in the center. Remove from the water bath and let it cool to room temperature, then refrigerate for at least 6 hours or overnight.
To unmold, run a thin spatula around the edges of the flan. Place a serving plate upside down on top of the pan and quickly flip. The flan will drop onto the plate and the caramel will pool around it beautifully.
