Whisk together flour, baking soda, and salt in a medium bowl, then set aside. In a large bowl, cream softened butter and granulated sugar until light and fluffy.

Beat in the egg and 1 tsp vanilla extract until well combined. Gradually add the dry ingredients to the wet, mixing on low speed until just combined without overmixing.

In a separate medium bowl, beat the softened cream cheese until smooth. Gradually add powdered sugar and 1 tsp vanilla extract, beating until creamy and well combined.

Preheat oven to 350°F (175°C) and line a baking sheet with parchment paper. Take small, rounded spoonfuls (about 1 tablespoon) of dough, flatten them, and place half on the baking sheet for bases.

Spoon 1-2 teaspoons of cheesecake filling onto each cookie dough base. Gently flatten remaining dough over the filling, sealing the edges to enclose it completely.

Bake for 10-12 minutes until edges are lightly golden, even if centers look soft. Let them cool on the baking sheet for a few minutes before transferring to a wire rack to cool completely, allowing the filling to firm up.