Preheat your oven to 325°F (160°C). Prepare a 9-inch springform pan by combining graham cracker crumbs, brown sugar, and melted butter in a bowl. Press the mixture firmly into the base of the pan to form an even crust. Bake for 10 minutes to set the base, then remove from the oven and set aside.

In a large mixing bowl, beat the softened cream cheese with granulated sugar, flour, and vanilla extract until the mixture is smooth and creamy. Add the eggs one at a time, mixing on low speed after each addition just until incorporated to avoid overmixing.

Gently fold in the citrus zest and juice, ensuring a balanced blend of lemon, lime, and orange flavors. Pour the cheesecake batter over the pre-baked crust, spreading it evenly.

Bake the cheesecake for approximately 1 hour and 5 minutes, or until the center is just slightly jiggly and the edges appear set. Once baked, run a knife around the edges of the pan to loosen the cheesecake. Allow it to cool completely at room temperature before removing the springform rim.

Transfer the cheesecake to the refrigerator and chill for at least 4 hours, or until thoroughly set. Slice and serve chilled for the best flavor and texture.