In a medium bowl, mix graham cracker crumbs with melted butter until evenly combined. Press into the bottom of a 9-inch springform pan to form the crust. Chill in the fridge while you prepare the filling.
Dissolve gelatin in boiling water, whisking until completely dissolved. Let it cool slightly.
In a large mixing bowl, beat cream cheese, sugar, and vanilla until smooth. Add yogurt and mix until creamy.
Slowly pour the cooled gelatin into the yogurt mixture while mixing continuously.
Pour the mixture over the chilled crust and smooth the top with a spatula.
Refrigerate for at least 4 hours, or until firm. Overnight is even better.
Top with fresh fruit before serving, if desired.