Combine gingersnap cookie crumbs and melted butter in a bowl; mix until well combined. Press into the bottom of 9-inch cake pan.
Bake in the preheated oven for 10 minutes; let cool, about 10 minutes.
Puree 1 mango using a food processor. Slice the other mango and arrange in an even layer over the cooled crust.
Beat the cream cheese, white sugar, and cornstarch in a bowl using an electric mixer on low speed until smooth and fluffy. Beat in the eggs 1 at a time, beating well after each addition. Add mango puree; mix on low speed until combined. Mix by hand to finish. Pour batter into cake pan.
Bake in the preheated oven until set, 55 to 65 minutes.
Turn oven off; let cake stand for 30 minutes in the oven with the door open 4 inches. Remove from oven; refrigerate.
