Preheat the oven to 325°F (163°C).
In a medium bowl, combine graham cracker crumbs, 1/4 cup granulated sugar, and melted butter. Mix until the crumbs are evenly coated.
Press the crumb mixture firmly into the bottom of a 9-inch springform pan to form an even crust layer.
Bake the crust in the preheated oven for 10 minutes. Remove and set aside to cool slightly.
In a large mixing bowl, beat the softened cream cheese with an electric mixer until smooth and creamy.
Add the Greek yogurt and 3/4 cup granulated sugar to the cream cheese and continue beating until well combined.
Add eggs one at a time, beating on low speed after each addition until just combined.
Mix in the vanilla extract, all-purpose flour, and salt until the batter is smooth and uniform.
Pour the cream cheese mixture over the cooled crust in the springform pan and spread evenly.
Bake the cheesecake for 45-50 minutes, or until the center is set but still slightly jiggly.
Turn off the oven and leave the cheesecake inside with the door slightly open for 1 hour to cool gradually.
Remove the cheesecake from the oven and refrigerate for at least 4 hours or overnight before serving.
Run a knife around the edges before releasing the springform pan to serve.