Preheat the oven to 300°F (150°C). Line the bottom and two sides of an 8-inch (20-cm) square baking dish with a sheet of aluminum foil, pressing it in firmly and allowing a 2-inch (5-cm) overhang on both sides. Line the baking dish with a second sheet of aluminum foil in the opposite direction (perpendicular to the first sheet), again allowing a 2-inch (5-cm) overhang on both sides.
Make the crust: In a bowl, whisk together the pistachio meal, sugar, and flour until well blended. Scatter the butter over the pistachio-flour mixture and, using your fingers or a pastry blender, work in the butter until the mixture is somewhat crumbly. Gather the dough into a tight ball.
Transfer the dough to the prepared baking dish. Using your fingers, press the dough firmly and evenly onto the bottom of the dish. Set aside.
Make the filling: Set two large bowls side by side. Separate the eggs, dropping the whites into one bowl and the yolks into the second bowl.
Grate the zest from two limes and squeeze 2 tablespoons of juice into the bowl with the yolks. Add the sour cream, vanilla, sugar, flour, and salt. Using an electric mixer, beat on medium speed until smooth.
Add the cream cheese, a few pieces at a time, and beat until smooth. Then add the Neufchâtel the same way, again beating until smooth.
Using clean beaters, beat the egg whites on high speed until stiff peaks form. Fold the egg whites, a little at a time, into the sour cream mixture. Pour or spoon the mixture into the prepared baking dish. Lift the baking dish and then gently tap it on the work surface to settle the filling. Using a rubber spatula, smooth the surface.
Bake the cheesecake until the center barely jiggles when the dish is shaken and a toothpick inserted into the center comes out almost clean, about 1 hour. Turn off the oven, crack the oven door, and leave the cake in the oven to cool for 1 hour longer.
Transfer the cake to a wire rack and let cool completely. Grasping the edges of the bottom layer of foil in both hands, lift the cheesecake out of the pan and place it on a work surface.
Top the cake: Using a rubber spatula, spread the top of the cake evenly with the sour cream. Have ready a tall glass of hot water. Dip a sharp knife into the hot water, dry the blade, and cut the cake into 9 equal pieces, rinsing the knife in the hot water and drying it after each cut. Cut the lime slices into quarters; you’ll need only 9 quarters. Garnish each cake square with a lime quarter, then sprinkle with the pistachios.
Use an offset spatula to transfer the cheesecake squares to a platter. Serve immediately, or cover loosely with plastic wrap and refrigerate for up to 2 days.