To core apple: Use an apple core tool to cut the apple down the middle, from the stem end, being careful not to press through the whole apple.
Use a melon baller to remove the top ¾ of the core, leaving the bottom of the apple’s core intact. Be sure to remove the tough fibers and seeds. To make the filling: Use a knife to mince the prosciutto chips, pistachio nuts and dates, and toss with the grated ginger and honey. This will form a sticky compote.
Fill the cored apples with the minced mixture using 2 spoons—1 to hold the filling and the other to scrape it into the apple.