If you plan to unmold the panna cotta onto plates, lightly grease the inside of the glasses with vegetable oil. Otherwise, you can leave them uncoated.
In a small bowl, soak the gelatin sheets in cold water until soft. Set aside.
Place heavy cream and granulated sugar in a small saucepan over medium heat and cook until just simmer (do not boil).
Squeeze gelatin to remove any excess water and add it to the pan, stirring constantly until the gelatin is melted.
Let the mixture cool until it is warm when touched. Gently whisk in the yogurt and vanilla extract into the cream mixture.
Pour the mixture evenly among the prepared moulds. Refrigerate until set for at least 4 hours.