In a 6-quart Dutch oven or wide, heavy saucepan large enough to accommodate all of the apples, combine the juice, cardamom, cinnamon, and a generous pinch of salt. Boil uncovered, over high heat, until the liquid is reduced by about half. Add the apples, mix well to coat with juice, and simmer, covered, until they are very tender, about 25 minutes depending on the variety of apples. Stir them from time to time, and, if necessary, add a bit more juice to prevent sticking.
The sauce should be thick and pulpy with little liquid visible. If necessary, boil it down for a few minutes, uncovered. Pick out and discard the cardamom and cinnamon. Put the sauce through a food mill or force it through a colander or strainer to remove the skins. Or if you used peeled apples, process in a food processor until smooth or leave somewhat chunky, according to preference.
Transfer the sauce to a bowl. Stir in 2 tablespoons pomegranate molasses or ourt and taste. Add a little more if you want the sauce tarter. (If this is your first time using pomegranate molasses or ourt, you may want to start with less.)
You can serve the sauce chilled, but it is also excellent at room temperature or warm from the pot with briskets, pot roasts, or latkes.