In a medium bowl, combine cream cheese and sugar until fluffy and incorporated. Add egg, and beat until combined.
Add vanilla and Greek yogurt (or sour cream) and mix until smooth. Pour into crust.
Spoon globs of Nutella caramel sauce onto cheesecake batter, dotting throughout the mixture. With a skewer, toothpick, or tip of a knife, carefully swirl caramel throughout cheesecake to create marbleized effect.
Bake at 350°F for 30-35 minutes, until filling is just set. (It will wobble slightly but should not be too wet.) If caramel is cooking too rapidly or becoming too bubbly, cover lightly with a sheet of foil for the last 10 minutes.
Cool to room temperature, then refrigerate and let cool completely before cutting into bars.