Preheat your oven to 350°F.
In a bowl, mix gluten-free graham cracker crumbs, 1 tablespoon sugar, and melted butter until the consistency resembles wet sand. Add more butter if it seems dry.
Press the crumb mixture into the bottom of a 9-inch springform pan.
Bake the crust for 10 minutes, then remove from oven and let it cool. Reduce oven to 300°F.
In a large mixing bowl, beat the softened cream cheese and 3/4 cup sugar until smooth.
Mix in the sour cream, vanilla extract, and cornstarch until well combined.
Add the eggs one at a time, mixing on low speed after each just until blended.
Pour the filling over the cooled crust.
Bake for 55–60 minutes, or until the center is almost set.
Turn off the oven and let the cheesecake sit inside for another hour.
Run a knife around the edge of the pan to loosen the cheesecake.
Let the cheesecake cool completely at room temperature.
Refrigerate for at least 4 hours or overnight before serving. Serve with whipped cream and fruit if desired.