Combine 1/3 cup of heavy whipping cream and gelatin powder in a small bowl, whisking immediately until combined. Set aside to thicken for a few minutes.
In a medium saucepan, combine the remaining 1 1/3 cups of heavy whipping cream, sugar-free vanilla syrup, and sea salt. Heat over medium-low heat, whisking constantly for about 5 minutes, until smooth and just beginning to bubble gently around the edges. Avoid a rolling boil.
In a separate bowl, lightly whisk the egg yolks. Slowly and gradually pour a small amount of the hot cream mixture into the egg yolks while continuously whisking to temper them and prevent scrambling. Continue adding the hot cream mixture until thoroughly combined.
Stir the bloomed gelatin mixture into the warm pudding mixture. Whisk well until the gelatin is completely dissolved and the mixture is smooth.
Let the pudding cool for about 10 minutes until lukewarm. Whisk again to remove any film. Press plastic wrap directly onto the surface of the pudding to prevent a skin from forming, then refrigerate for at least 4 hours, or until fully firm and set.
Once chilled and firm, give the pudding a good stir or whip it with a hand mixer for a minute or two to make it wonderfully light and silky smooth before serving.