In a small bowl, mix the brown sugar and cinnamon. Stir in the melted butter until a thick, spreadable paste forms. It should hold its shape when stirred. Set aside.

Whisk the flour, baking soda, baking powder, and salt together in a separate bowl to ensure even distribution and tender cookies.

In a large bowl, beat the softened butter with both sugars for 2–3 minutes until pale and fluffy. Add the egg, egg yolk, and vanilla, mixing until smooth and glossy.

Gradually add the dry ingredients to the butter mixture and mix just until a dough forms. If the dough feels sticky, chill it for 10 minutes instead of adding extra flour.

Gently fold the cinnamon mixture into the dough using a spatula. Stop early so visible cinnamon ribbons remain rather than fully blending it in.

Scoop about 2 tablespoons of dough and flatten it slightly in your palm. Place a frozen cheesecake portion in the center, wrap the dough around it completely, and roll into a smooth ball with no filling exposed.

Refrigerate the assembled cookie balls for at least 1 hour. Chilled dough spreads less and bakes up thicker.

Preheat the oven to 350°F and line baking sheets with parchment paper. Place cookies about 2½ inches apart and bake for 12–15 minutes, until the edges are lightly golden and the centers still look soft. They will continue to set as they cool.

Let the cookies cool on the baking sheet for 5 minutes, then transfer to a rack. Whisk powdered sugar, milk, and vanilla until smooth and drizzle lightly over fully cooled cookies.