Preheat oven to 350°F (175°C). Wrap the bottom and sides of a 9-inch springform pan tightly with heavy-duty aluminum foil to prevent water bath leakage.

In a medium bowl, combine graham cracker crumbs and 1/4 cup granulated sugar. Pour in the melted butter and mix until all crumbs are moistened.

Press the crumb mixture evenly into the bottom and slightly up the sides (about 1 inch) of the prepared springform pan.

Bake the crust for 8-10 minutes, until lightly golden. Remove from oven and let cool slightly while preparing the filling. Reduce oven temperature to 325°F (160°C).

In the bowl of a stand mixer fitted with the paddle attachment (or using an electric hand mixer), beat the softened cream cheese on medium speed until smooth and creamy, about 3-4 minutes, scraping down the sides of the bowl as needed.

Gradually add 1 1/2 cups granulated sugar to the cream cheese, beating until well combined and fluffy, about 2-3 minutes.

Add the fresh key lime juice and key lime zest. Beat on low speed until just incorporated. Do not overmix.

Beat in the heavy cream and vanilla extract until just combined.

Add the eggs one at a time, beating on low speed only until each egg is just incorporated before adding the next. Overmixing after adding eggs can introduce too much air, leading to cracks. Scrape down the bowl as needed to ensure everything is mixed evenly.

Pour the cheesecake filling over the cooled graham cracker crust in the springform pan. Gently tap the pan on the counter a few times to release any air bubbles.

Place the foil-wrapped springform pan into a larger roasting pan. Carefully pour hot water into the roasting pan until it comes about halfway up the sides of the springform pan. This water bath helps ensure even baking and prevents cracks.

Carefully transfer the roasting pan with the cheesecake to the preheated oven (325°F/160°C).

Bake for 50-65 minutes, or until the edges are set but the center 2-3 inches still jiggles slightly when gently shaken. Do not overbake.

Turn off the oven, crack the door open slightly, and leave the cheesecake in the water bath for another 1 hour to cool gradually. This helps prevent cracking.

Carefully remove the cheesecake from the water bath and remove the foil. Let it cool completely on a wire rack at room temperature for about 1-2 hours.

Once completely cooled, cover the cheesecake loosely with plastic wrap and refrigerate for at least 4 hours, or preferably overnight, to allow it to firm up and flavors to meld.

To serve, run a thin knife around the edge of the pan before releasing the springform collar. Garnish with additional key lime zest or thin key lime slices, and a dollop of whipped cream, if desired.