Bloom the gelatin by sprinkling it over 1 tablespoon of cold water in a small ramekin and let it sit for 5 minutes.
In a separate small bowl, dissolve the espresso powder in 2 tablespoons of hot water and set aside.
Place the egg yolks and granulated sugar in a heat-proof glass bowl set over a saucepan of simmering water (bain-marie), ensuring the bottom of the bowl does not touch the water.
Whisk the yolk mixture continuously for 5 to 7 minutes until it becomes pale, thick, and reaches a temperature of 160°F (71°C).
Stir the bloomed gelatin and the dissolved espresso into the warm yolk mixture until the gelatin has completely melted and the mixture is smooth.
Remove the bowl from the heat, stir in the vanilla extract and salt, then allow the mixture to cool to room temperature (approximately 20 minutes).
In a separate chilled bowl, whip the heavy cream until stiff peaks form, being careful not to overbeat.
Gently whisk one-third of the whipped cream into the cooled coffee base to lighten the density.
Using a silicone spatula, fold the remaining whipped cream into the mixture using a slow figure-eight motion until no white streaks remain.
Transfer the mousse into individual serving glasses and refrigerate for at least 3 hours to allow the structure to set before serving.