Lightly grease the bottom of a 10-inch springform pan with butter. Do not grease the sides of the pan. Wrap the outside of the pan with foil to prevent leakage. In a food processor, fitted with the steel blade attachment, pulverize the graham craham crackers into crumbs. Transfer the crumbs to a mixing bowl. Add the melted butter and mix with a rubber spatula. Press the crumb mixture over the bottom of the springform pan, reaching all the way to the sides so it forms a seal against leakage. Bake for 10 minutes, remove and cook whle you make the filling; lower the heat to 325F.
FOR THE FILLING AND TOPPING: With an electric mixer on low speed, beat the cream cheese and sugar for 2 minutes or until soft and creamy. Add the eggs, one at a time, beating for 15 seconds between additions to make sure each one is thoroughy incorporated. Scrape down the sides of the bowl, with a rubber spatula and beat for a minute longer. With the machine running, slowly beat in in the half-and-half and then 2 tablespoons Key lime juice. Set aside 1/2 cup of the cheesecake mixture to which you should add the remaining Key lime juice and transfer this to a liquid measuring cup or pitcher.
FOR THE CAKE: Pour the cheesecake mixtue over the baked crust, then por a thin stream of Key Lime-boosted cheesecake mixture over the top and scatter the grated lime zest over that. With a toothpick or wooden skewer, swirl the Key lime mixture and zest into the batter the way you would marbelize a cake. Bake for 1 1/2 hours or until the mixture is set; the cake will appear to be jiggly, but will firm up upon standing.
TO SERVE: Remove the cake from the oven and place on a rack ro cool to room temperature in the pan. Unlock the springform and remove the cake, but leave the cake on the bottom of the pan. . Chill in the refrigerator for at least 4 hours before serving or before attempting to remove the cake from the springform bottom.