Soak the gelatin sheets in cold water for 5–10 minutes until soft.
In a saucepan, combine the heavy cream, milk (or espresso), sugar, espresso powder, and a pinch of salt. Heat gently, stirring, until the sugar dissolves and the mixture is steaming.
Take the pan off the heat. Squeeze the excess water out of the gelatin sheets and stir them into the warm cream until fully dissolved.
Stir in the vanilla.
Pour into 6 glasses or ramekins. Let them cool a bit at room temperature, then refrigerate for at least 4 hours, until set.