I always start by roasting whole sweet potatoes at 400°F for about 45 minutes until they're fork-tender. Once cooled, I peel off the skin and blend the flesh until it's completely smooth. This step genuinely changes the final texture compared to using canned filling.
Pulse the gingersnap cookies in a food processor until they turn into fine crumbs, then mix them with melted butter and brown sugar. Press this mixture firmly into the bottom of your springform pan using the back of a spoon. Bake it alone for 8 minutes so it sets before the filling goes in.
In a stand mixer, beat the softened cream cheese on medium speed until it's completely smooth with zero lumps. This usually takes about 2 minutes, and it's the step I never rush because lumps here never go away later.
Slowly add the granulated sugar, then mix in the sweet potato puree until the color turns a consistent orange-tan throughout. Scrape down the sides of the bowl so nothing hides at the bottom unmixed.
Add the eggs one by one, mixing on low speed just until each one disappears into the batter. Overbeating at this stage adds too much air, which is one of the top reasons cheesecakes crack in the oven.
Gently fold in the sour cream, vanilla extract, pumpkin pie spice, salt, and cornstarch using a spatula. This keeps the batter dense and silky rather than airy and loose.
Wrap the outside of your springform pan tightly in two layers of foil, then place it inside a larger roasting pan. Pour hot water into the roasting pan until it reaches about halfway up the sides of the springform pan.
Bake at 325°F for 60 to 70 minutes, until the edges look set but the center still has a slight jiggle. Turn off the oven and let the cheesecake sit inside with the door cracked open for an extra hour.
Once it's cool enough to handle, move it to the refrigerator uncovered for about an hour, then cover it and chill for at least 5 to 6 hours, though overnight is honestly best. This resting time is what gives it that dense, sliceable texture.