Carefully cut each strawberry from the tip until you almost reach the stem. If you want, you can cut in the opposition direction, forming an "X" (this can help with smaller berries). Set the berries aside.

In a small mixing bowl, whip together the cream cheese, powdered sugar, caramel sauce, and kosher salt until light and fluffy, then spoon the mixture into a small decorating bag. In another small decorating bag, place the 1/2 cup of chocolate hazelnut spread.  Flatten out each bag and place them on top of each other, then snip off about 1" of the bags. Place the two flattened bags inside another decorating bag fitted with a large Wilton tip (like 1M). Squeeze the bag just enough so both of the fillings are coming out at the same time. (For detailed directions with pictures on this process, check out this post.)

Carefully place the tip into the bottom of each cut strawberry and squeeze the filling into each berry being careful not to overfill. Serve immediately.