In a small bowl, sprinkle the gelatin over the cold water and let it sit for about 5 minutes to bloom.

In a saucepan over medium heat, combine the heavy cream, brewed coffee, sugar, and salt. Stir until the sugar is dissolved and the mixture is heated through, but do not let it boil.

Remove the saucepan from heat and stir in the bloomed gelatin until fully dissolved. Add the vanilla extract and mix well.

Pour the mixture into individual serving cups or ramekins.

Allow the panna cotta to cool at room temperature for about 30 minutes, then cover and refrigerate for at least 4 hours or until set.

To serve, run a knife around the edges of the panna cotta and gently invert onto a plate, or serve directly in the cups.