Step 1: Prepare the Cheesecake Filling

1. In a small bowl, beat cream cheese, powdered sugar, and vanilla extract until smooth.
2. Scoop teaspoon-sized portions onto a parchment-lined baking sheet and freeze for at least 30 minutes.

Step 2: Make the Cookie Dough

1. Preheat oven to 350°F (175°C) and line a baking sheet with parchment paper.
2. In a medium bowl, whisk together flour, baking soda, and salt.
3. In a large bowl, cream together butter, brown sugar, and granulated sugar until light and fluffy.
4. Beat in the egg, vanilla extract, and milk until combined.
5. Gradually add dry ingredients to the wet ingredients, mixing until just incorporated.

Step 3: Assemble the Cookies

1. Scoop a tablespoon of dough, flatten slightly, and place a frozen cheesecake filling in the center.
2. Cover with another flattened piece of dough, sealing the edges.
3. Place cookies 2 inches apart on the prepared baking sheet.
4. Bake for 10-12 minutes until edges are lightly golden.

Step 4: Add the Caramel Drizzle

1. Let cookies cool on the baking sheet for 5 minutes, then transfer to a wire rack.
2. Drizzle warm caramel sauce over each cookie.
3. Sprinkle with sea salt if desired.