Preheat your oven to 350°F (175°C) and line a baking sheet with parchment paper or a silicone baking mat.

1. In a large mixing bowl, beat together the softened butter and granulated sugar until light and fluffy, about 2-3 minutes.
2. Add the egg and vanilla extract, and mix until fully incorporated.
3. In a separate bowl, whisk together the all-purpose flour, baking soda, and salt.
4. Gradually add the dry ingredients to the wet ingredients, mixing until just combined. The dough should be thick but pliable.
5. In a medium bowl, beat together the cream cheese, granulated sugar, vanilla extract, and flour until smooth and creamy. The filling should be thick enough to spoon but still spreadable.
6. In a small bowl, combine the graham cracker crumbs, melted butter, and sugar. Stir until the mixture is well combined and crumbly.
7. Scoop about 2 tablespoons of dough and roll it into a ball. Place the dough balls onto the prepared baking sheet, spacing them about 2 inches apart. Press each dough ball slightly to flatten.
8. Create a small indentation in the center of each dough ball using your finger or the back of a spoon. Spoon about 1 teaspoon of cheesecake filling into the indentation of each cookie dough ball.
9. Top with the graham cracker crumble, pressing it down lightly to help it stick.
10. Bake for 10-12 minutes, or until the edges are golden brown but the centers are still soft. Be careful not to overbake them.
11. Allow the cookies to cool on the baking sheet for 5 minutes before transferring them to a wire rack to cool completely.
12. Serve and enjoy your New York Cheesecake Cookies!