Soak the gelatin sheets in cold water for 5 minutes until softened.
In a saucepan over medium heat, combine whole milk and granulated sugar, stirring until dissolved but not boiling.
Whisk egg yolks in a separate bowl until pale and thickened.
Slowly pour half of the hot milk mixture into the egg yolks while whisking to temper them.
Return the mixture to the saucepan and cook on low heat, stirring constantly until it thickens enough to coat the back of a spoon (about 5 minutes).
Remove from heat and stir in softened gelatin sheets and vanilla extract until well combined.
Let cool slightly before folding in whipped heavy cream. Transfer to serving dishes or molds and refrigerate for at least 4 hours until set.