Heat oven to 325°F (163°C) and set a rack in the lower third. Butter the inside of a 9-inch springform pan and line the base with parchment. Wrap the outside with two or three layers of heavy-duty foil, running it at least 2 inches up the sides, then boil a full kettle of water and set it aside.
Pulse the graham crackers in a food processor until fine and sandy, about 1½ cups (150g). Add the 2 tablespoons (25g) sugar and a pinch of salt and pulse to mix, then pour in the 6 tablespoons (85g) melted butter and pulse until the crumbs look like wet sand. Tip into the pan and press firmly across the base and about ½ inch up the sides using the flat bottom of a measuring cup.
Bake the crust for 8 to 10 minutes, until it smells toasty and looks set. Set it on a rack to cool while you make the filling, leaving the oven on at 325°F (163°C).
Beat the 32 oz (900g) softened cream cheese on low speed until completely smooth, scraping the bowl often. Add the 1 cup (200g) granulated sugar and the 1 tablespoon (8g) cornstarch, then beat on low until just combined, keeping the speed low the whole time since beating air into the batter is what causes cracks.
Mix in the ½ cup (120g) sour cream and ⅓ cup (80ml) heavy cream on low until smooth. Add the 1 tablespoon vanilla bean paste and beat just until the flecks spread through the batter, then scrape the bowl down one more time to catch any hidden lumps of cream cheese.
Add the 3 whole eggs and 2 egg yolks one at a time, mixing on low after each just until it disappears. Stop mixing the moment the last yolk blends in, and if the batter looks airy, tap the bowl on the counter a few times to release bubbles.
Pour the filling over the cooled crust and smooth the top with an offset spatula. Set the foil-wrapped pan inside a large roasting pan, then pour the hot kettle water into the roasting pan until it reaches halfway up the springform sides.
Bake at 325°F (163°C) for 1 hour to 1 hour 15 minutes. The edges should look set while the center still wobbles slightly when you nudge the pan, and avoid opening the door for the first 50 minutes since a temperature drop can crack the top.
Turn off the oven and crack the door open a few inches. Leave the cheesecake inside for 1 hour to cool slowly, then lift the pan out of the water bath, remove the foil, and let it finish cooling on the counter to room temperature.
Cover the pan loosely and refrigerate for at least 6 hours, or overnight for the cleanest slices. Keep the top uncovered for the first hour of chilling so condensation does not collect on the surface, since a dry, cold surface is what you need for the sugar to caramelize properly.
Just before serving, run a thin knife around the edge and release the springform ring. Blot the surface dry with a paper towel, then sprinkle the ⅓ cup (65g) sugar in a thin, even layer. Hold the torch a few inches away and move it in small circles until the sugar melts and turns deep amber, then let the caramel set for 2 to 3 minutes until it hardens before slicing and serving.