Preheat your oven to 350°F. Wrap the outside bottom and sides of a 9-inch springform pan securely with two large sheets of heavy-duty aluminum foil, bringing the foil all the way up to the top rim to create a completely waterproof barrier for the water bath.

In a medium mixing bowl, combine the graham cracker crumbs, ¼ cup of granulated sugar, and melted unsalted butter. Stir firmly with a spoon until the crumbs are completely moistened and resemble wet sand.

Dump the crumb mixture into your prepared springform pan. Use the flat bottom of a measuring cup or your hands to firmly compress the mixture into a tight, even layer across the bottom and up to 1 inch up the sides of the pan. Bake the crust for exactly 10 minutes at 350°F, then remove and set aside to cool completely.

Reduce the oven temperature to 325°F. In an extra-large mixing bowl, combine the room-temperature cream cheese, 1 ¼ cups of granulated sugar, and all-purpose flour.

Use an electric mixer set to low speed, beating for 1 to 2 minutes just until the ingredients are completely smooth and free of lumps. Scrape down the sides of the bowl frequently; keeping the mixer on low speed prevents excess air from being whipped into the fats.

Add the room-temperature sour cream and vanilla extract straight into the cheese bowl, mixing on low speed for 30 seconds until fully incorporated.

Add the eggs one at a time, mixing on low speed after each addition just until the yellow yolk disappears into the batter. Avoid over-beating at this stage, as over-mixing will cause the cheesecake to puff up violently in the oven and crack across the center as it cools.

Pour the smooth cream cheese batter directly over the cooled graham cracker crust. Place the wrapped springform pan inside a large, deep roasting pan, and slide the assembly onto the middle oven rack.

Carefully pour hot boiling water into the outer roasting pan until the liquid reaches about halfway up the sides of the springform pan, taking care not to splash any water inside the cake.

Bake at 325°F for 1 hour and 15 minutes. Watch the center closely; the cheesecake is finished the exact moment the outer borders are set and stable, and the very center gives a slight, firm jiggle when the pan is moved.

Turn off the oven burner completely. Crack the oven door open about an inch and leave the cheesecake sitting inside the water bath undisturbed for 1 full hour. This gradual drop in temperature allows the dairy proteins to cool slowly, preventing structural shock and surface cracks.

Lift the pan out of the water bath, remove the aluminum foil sheets, and place the cake on a wire rack. Run a thin, warm butter knife gently around the inside edges of the pan to loosen the crust from the sides. Let it cool completely to room temperature, then cover tightly and transfer to the refrigerator to chill for at least 6 hours (or ideally overnight) to set into a dense, clean sliceable texture.