For best results, let your eggs, cream cheese, and ricotta warm to room temperature.
To make your own applesauce, first peel, core, and chop the apples. Cook them over low heat in a small covered pot with a few tablespoons of water until soft (you may need a little more or less water depending on the type of apple you use). Mash or blend the cooked apples to make a sauce. Set aside 1 cup of the resulting mixture and allow it to cool. Alternatively, you can use a prepared unsweetened applesauce.
Preheat oven to 350°F (176°C) and boil a large kettle or pot of water.
Line the inner walls of the pan with long strips of parchment paper. You can grease the surface with butter instead, but parchment paper is much more foolproof.
Combine the pumpkin puree, cream cheese, ricotta, and sugar in a stand mixer equipped with a paddle, or in a large bowl with a hand mixer. Combine at moderate speed, taking care not to whip too much air into the mixture.
Add the eggs one at a time, pausing to allow them to combine well with the remaining ingredients. Add 1 cup of applesauce and the spices, and mix until well combined.
Wrap the bottom and sides of the pan in aluminum foil to create a relatively tight seal. Place the foil-wrapped pan into the center of a roasting pan or other large oven safe dish with high sides.
Pour the filling into the crust carefully. Pour enough hot water into the roasting pan to submerge the foil-wrapped cake pan to about the half-way point. Bake at 350°F for about 90 minutes, or until just barely set in the center.
Remove the cake from the oven and from the hot-water bath. Set aside to cool, then cover with foil and refrigerate for at least 8 hours.