Place a large mixing bowl and whisk attachment in the freezer for 15 minutes.
In a small saucepan, pour ¼ cup cold water. Sprinkle gelatin evenly over the surface. Whisk gently and let stand for 5 minutes to bloom.
Over low heat, gently warm the gelatin mixture for 1-2 minutes, whisking constantly, until gelatin is fully dissolved. Remove from heat, add instant espresso powder, and whisk until smooth. Set aside to cool for 5 minutes.
Retrieve chilled bowl and whisk. Pour in cold heavy cream, sugar, and vanilla extract. Beat on medium-high speed for 2-3 minutes until soft peaks form.
With mixer running on low speed, slowly drizzle the slightly cooled coffee-gelatin mixture into the whipped cream. Continue beating for 20-30 seconds until evenly colored. Fold any streaks from the bottom with a spatula.
Divide mousse among 4 serving cups. Cover loosely with plastic wrap and refrigerate for at least 2 hours, or up to overnight. Serve cold.