How to Make It
Whisk together the sugar, cornstarch, and salt in a large pot. Gradually whisk in the egg yolks, then the milk and ½ cup of the heavy cream.
Cook over medium-high heat, whisking constantly, until thickened and beginning to bubble, 4 to 5 minutes. Reduce heat to medium-low and cook, whisking constantly, until the pudding starts to pull away from the edge of the saucepan, 1 minute more. Remove from heat and pour through a fine-mesh sieve into a clean bowl, pushing the pudding through gently with a spatula or spoon. Add the butter and vanilla and stir until melted.
Cover with plastic wrap (directly on the surface of the pudding) and refrigerate until cold and firm, at least 3 hours.
Beat the remaining 1½ cups of heavy cream with an electric mixer until soft peaks form, 2 to 4 minutes. Fold the cream into the pudding mixture.
Line the bottom of a 2-quart serving dish or a large bowl with half the gingersnaps. Top with half the bananas, then half the pudding; repeat. Cover tightly with plastic wrap and refrigerate for at least 4 hours.
Just before serving, top with the gingersnap crumbs. Serve drizzled with the Banana Caramel.