Line two large baking sheets with parchment paper. Set aside.
To make the cream cheese filling, beat the cream cheese in a large bowl with an electric mixer or stand mixer fitted with the paddle attachment until smooth. Add the confectioners' sugar, flour, and vanilla and beat on low speed to combine then increase the speed to high and beat until smooth and fluffy.
Drop the cheesecake filling by a teaspoonful on one of the prepared cookie sheets. Place them in the freezer while you make the dough.
To make the cookie dough, whisk the flour, baking soda, and salt in a medium bowl.
In the bowl of a stand mixer or large bowl with the paddle attachment, cream butter, and sugar on high speed until light and fluffy, 2-3 minutes. Do not skip this step. Add the egg and vanilla extract and beat again for 1-2 minutes.
Slowly add the dry ingredients and beat on low speed to mix then turn it up to medium-high to combine.
Scoop 1 tablespoon of the dough out and roll it into balls and place on the other prepared cookie sheet. Use your thumb to make an indent in the middle of each cookie ball. Remove the cheesecake filling from the freezer and place cheesecake ball in the center of half of the cookie dough balls. Top with the remaining cookie dough balls then pinch the seems and roll into a ball or taller cone shape. Place on the cookie sheet 3 inches apart. Chill in the fridge for at least 2 hours, or up to 3 days. You can put them in the freezer for an hour if you're in a rush.
Preheat the oven to 350°F.
Bake the chilled cookies for 9-11 minutes, or until the tops are just set. Remove from the oven and allow to cool on the baking sheet for 5 minutes then transfer to a cooling rack to cool completely.
While they’re cooling, make the caramel topping. Place the unwrapped caramels and heavy cream in a microwave-safe bowl. Microwave for 30 seconds, then stir and continue to microwave in 15-second intervals until melted and bubbling. Stir until smooth. Use a spoon to drizzle the melted caramel over each cookie. If the caramel begins to thicken as you work, microwave again in 15-second increments.