Make the Cheesecake Filling:

1. Prepare the Filling: In a medium mixing bowl, beat the softened cream cheese with ¼ cup of sugar until smooth and creamy. Add the egg yolk and vanilla extract, mixing well until fully combined. Set the filling aside and chill it in the refrigerator while you prepare the cookie dough.

Prepare the Snickerdoodle Dough:

2. Mix the Dry Ingredients: In a medium bowl, whisk together the flour, cream of tartar, baking soda, salt, and cinnamon. Set this mixture aside.
3. Cream the Butter and Sugar: In a large mixing bowl, use an electric mixer to cream the softened butter and granulated sugar together until light and fluffy. This should take about 3-4 minutes.
4. Add the Egg and Vanilla: Beat in the egg and vanilla extract, mixing until fully combined.

Form the Snickerdoodle Cookies:

5. Combine Dry and Wet Ingredients: Gradually add the dry ingredient mixture to the wet ingredients, mixing on low speed until just combined. Be careful not to overmix the dough.
6. Chill the Dough: To make the dough easier to handle, refrigerate it for about 20 minutes to firm up slightly.
7. Preheat the Oven: While the dough is chilling, preheat your oven to 350°F (175°C) and line a baking sheet with parchment paper or a silicone baking mat.

Assemble the Cookies:

8. Shape the Dough: Once the dough has chilled, scoop out approximately 1 tablespoon of dough and roll it into a ball. Use your thumb to make a small indentation in the center of each dough ball.
9. Add the Cheesecake Filling: Take a small spoonful of the chilled cheesecake filling and place it in the center of the indentation in each dough ball. You can use about 1 teaspoon of filling per cookie.
10. Seal the Dough: Carefully pinch the edges of the dough around the cheesecake filling to seal it in. Roll the dough ball again to smooth out any seams.

Coat and Bake:

11. Cinnamon Sugar Coating: In a small bowl, mix together the 2 tablespoons of sugar and 1 teaspoon of cinnamon. Roll each stuffed dough ball in the cinnamon sugar mixture, ensuring it’s evenly coated.
12. Bake: Place the cookies on the prepared baking sheet, spacing them about 2 inches apart. Bake for 10-12 minutes, or until the edges of the cookies are golden brown, but the centers are still slightly soft.
13. Cool: Allow the cookies to cool on the baking sheet for 5 minutes before transferring them to a wire rack to cool completely.

Serve:

14. Enjoy: Once the cookies have cooled, serve them with a glass of milk or your favorite beverage. These cookies are best enjoyed fresh, but they can be stored for later.