Measure or weigh the powdered sugar into a small bowl and set it aside. In another bowl, measure or weigh the flour and baking powder, then whisk to blend.
Cube the butter into the mixer bowl and cream it for one minute. Add the cream cheese and blend on medium speed for about 1 minute. Stop the mixer, scrape down the sides, then turn it back on to low speed.
Gradually add the powdered sugar until incorporated, then turn the mixer to medium speed and mix for 3 minutes. Add the vanilla extract, then the egg, and mix until combined. Turn the mixer to low speed and add the flour mixture. Try not to overmix.
Remove the mixer bowl from the stand and, using a spatula, fold in the cherries and caramel chips until evenly distributed. Cover loosely and refrigerate for 1 hour.
Preheat the oven to 350°F (175°C or 180°C) and line two cookie pans with parchment paper. Pour the superfine sugar onto a flat plate.
Take the cookie dough out of the refrigerator, scoop using a medium cookie scoop, and roll into balls with your hands. Roll each ball in the superfine sugar and place twelve on a cookie sheet pan.
Bake for 11 to 13 minutes, then move to a cooling rack after removing them from the oven.