Place the softened butter and both sugars into a large bowl. Use your mixer to beat them until the mixture looks light and fluffy. This usually takes about three minutes.

Crack the egg into the bowl and add the vanilla extract. Mix again on medium speed until everything is combined. Scrape the sides of the bowl with your spatula to include everything.

In a separate bowl, whisk the flour, graham cracker crumbs, baking soda, and salt. Gradually add this dry mixture to the wet ingredients. Mix slowly until the flour just disappears.

Take your chilled cream cheese and cut it into small cubes. Carefully fold these cubes into the cookie dough. You want the bits of cream cheese to stay intact for the best texture.

Cover the bowl with plastic wrap and put it in the fridge. Let it rest for at least thirty minutes. Chilling the dough prevents the cookies from spreading too much in the oven.

Preheat your oven to 350°F. Use a cookie scoop to place round balls of dough onto your lined baking sheets. Leave about two inches of space between each cookie ball.

Slide the trays into the oven and bake for 10 to 12 minutes. The edges should be a light golden brown. The centers will still look a bit soft, which is perfect.

Once the cookies come out, immediately drizzle thick caramel sauce over the top. While the caramel is still wet, sprinkle a tiny bit of sea salt. This balances the sweet flavor.

Let the cookies sit on the hot baking sheet for five minutes. Then, move them to a wire rack to cool fully. The cheesecake bits will firm up as they cool down.