Preheat your oven to 325°F / 165°C.
In a medium bowl, combine the crushed gingersnaps and melted butter until the crumbs are evenly moistened. Firmly press this mixture into the bottom of a 10-inch springform pan.
Sprinkle the grated ginger and brown sugar evenly over the top, gently pressing it into the crust.
In the bowl of a stand mixer, or using a large bowl and a hand mixer, beat the room temperature cream cheese and granulated sugar on medium speed until completely smooth and no lumps remain. Scrape down the sides of the bowl.
Add the eggs one at a time, mixing on low speed until just combined after each addition.
Mix in the cornstarch, vanilla extract, and salt. Be careful not to overmix.
Using a spatula, gently fold in the shredded coconut and diced dried papaya by hand.
Pour half of the cheesecake batter over the prepared crust.
Sprinkle the sliced almonds in an even layer over the batter. Carefully pour the remaining batter on top.
Bake for 80-90 minutes, or until the edges are set and the center has a slight wobble.
Turn off the oven, crack the door open slightly, and let the cheesecake cool completely inside the oven for about an hour. This helps prevent cracking.
Once at room temperature, cover the cheesecake and refrigerate for at least 12 hours, or preferably overnight, before releasing from the pan, slicing, and serving.
Once the eggs are added, mix only until they are just combined. Overmixing incorporates too much air, which can cause the cheesecake to rise too quickly and then crack as it cools.