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. Then place panna cottas into the fridge to chill until set, about 4 hours.
