Whisk heavy cream, coffee, brown sugar, espresso powder, salt, and vanilla together in a saucepan. Heat over medium-low heat, stirring often, until mixture is hot and sugar and espresso powder have dissolved, 5 to 7 minutes; do not boil.

Meanwhile, place 1/2 cup whole milk in a small bowl. Sprinkle gelatin over the top and let sit for 5 minutes to allow gelatin to bloom.

Remove the pan from the heat. Whisk in bloomed gelatin and stir until completely dissolved and incorporated.

Place a fine mesh strainer over a large heat-safe measuring cup, or a large bowl, preferably with a pour spout. Carefully pour coffee mixture through the strainer.

Pour strained coffee mixture into glass serving dishes or ramekins, and allow to cool to room temperature, about 30 minutes.