Recreating an accidental crust effect
I have seen recipes where a hot caramel was poured on the crust before the filling is added. It's designed to help help keep the crust from becoming soggy.

Sadly, I can't find a recipe for you; googling turns up a lot of results for caramel sauces on top. But I can give you a basic approach:

Prepare your crust in the pan. Dissolve 1/2 cup sugar in 2 tablespoons of water. Bring to boil over high heat. Cook without stirring until it becomes a nice, rich brown (about 350 degrees). 

Pour the hot syrup over your crust, and tilt to cover the crust evenly. (You'll probably have more syrup than you really need.) Allow to cool (about 20 minutes) before pouring in the filling. Bake as before.

(Bonus: it helps to wrap a large, wide sheet of aluminum foil around your springform pan before putting your cake in the water bath, to prevent leaks.)