In a small microwave-safe bowl, place ¼ cup (60 grams) cold water. Sprinkle gelatin evenly on top; let stand until hydrated, 5 to 10 minutes.
Meanwhile, in a medium saucepan, whisk together cream, sugar, salt, and espresso powder; cook over medium heat, whisking frequently, until steaming. (Do not boil.) Remove from heat. Add chocolate hazelnut spread and finely chopped chocolate; whisk until melted and well combined. (If chocolate isn’t completely melted, return pan to stovetop, and cook over medium-low heat, whisking frequently, until mixture is smooth and well combined.)
Heat gelatin mixture on high in 10-second intervals, stirring between each, until gelatin completely dissolves. Gradually pour gelatin mixture into warm cream mixture, whisking constantly. Whisk in milk and vanilla.
Fill a large bowl with ice water. Strain cream mixture through a fine-mesh sieve into a medium metal bowl. Place bowl in prepared ice water bath; stir until an instant-read thermometer registers 70°F (21°C).
Divide cooled cream mixture among 6 serving glasses (about ¾ cup or 190 grams each); refrigerate, uncovered, for at least 4 hours or up to overnight. Serve with Vanilla Whipped Cream. Garnish with berries, if desired.