Preheat your oven to 350°F and lightly spray a 9-inch springform pan with non-stick cooking spray to facilitate a smooth vertical release.
Crush the graham crackers into ultra-fine crumbs using a food processor, or place them inside a large zip-top bag and roll firmly with a rolling pin.
In a large mixing bowl, combine the fine graham cracker crumbs, salt, ½ cup of the granulated sugar, and the melted unsalted butter. Stir firmly with a fork until the crumbs are uniformly saturated and resemble wet sand.
Measure out exactly 3 cups of the wet crumb mixture and transfer it into the prepared springform pan. Use the flat bottom of a dry measuring cup to press the crumbs firmly and evenly across the bottom and up the sides of the pan to build a solid foundational crust. Set the pan and the remaining 2 cups of loose crumbs aside.
In the bowl of a stand mixer fitted with the paddle attachment (or using an electric hand mixer), add the softened cream cheese, the remaining 1 ½ cups of granulated sugar, and the vanilla extract. Beat on medium-high speed for 2 to 3 minutes until completely smooth, velvety, and free of lumps.
Reduce the mixer speed to low. Add the room-temperature eggs one at a time, mixing just until each egg is integrated into the batter. Avoid over-beating at this stage, as incorporating too much air into the egg proteins will cause the cheesecake to puff up like a soufflé and crack during baking.
Gently pour the smooth cream cheese filling straight into the prepared bottom crust, using a spatula to level the surface flat.
Take the reserved 2 cups of buttery graham crumbs and scatter them uniformly across the entire top surface of the cream cheese filling. Pat down lightly with the back of a spoon to settle the top crust without pressing it deep into the batter.
Place the pan on the middle oven rack and bake at 350°F for 65 to 75 minutes. The cheesecake is finished when the outer edges look set and matte, while the very center retains a slight, gelatinous jiggle when the pan is gently tapped. (Alternatively, a digital instant-read thermometer inserted into the exact center should register 145°F).
Remove the cheesecake from the oven and set the springform pan flat on a wire rack to cool down to room temperature. Once cool, run a thin knife along the inside edge of the pan, wrap the top securely, and refrigerate for at least 4 hours (ideally overnight) to allow the lipid structures to firm completely before springing the outer ring, slicing, and serving.