Cut the tops and bottoms off of the persimmons and apples. Use a mandoline to thinly slice them into rounds, or, if you don't have a mandoline, do your best to thinly slice with a knife.
Once the fruit is sliced, stack the slices and cut the stack into quarters. Place in a medium salad bowl and set aside while you make the dressing.
In a small bowl, whisk together the olive oil, honey, fresh lime juice, and salt. Pour over the persimmons and apples, and use your hands to toss and make sure each piece is nicely coated with dressing.
Add the pomegranate arils and crumbled cheese, then toss lightly to combine. Serve right away.