Preheat your oven to 350°F (175°C) and prepare a baking sheet by lining it with parchment paper.
In a large mixing bowl, cream together the softened unsalted butter, granulated sugar, and packed brown sugar until light and fluffy, about 3-4 minutes.
Gradually add the eggs one at a time, ensuring each is well incorporated before adding the next. Mix in the pure vanilla extract until combined.
In a separate medium bowl, whisk together the all-purpose flour, sifted cocoa powder, baking soda, and fine sea salt until well combined.
Gradually add the dry mixture to the creamed butter and sugars, stirring until just combined. Gently fold in the semi-sweet chocolate chips with a spatula.
In another bowl, beat together the softened cream cheese, sifted powdered sugar, and fresh lemon juice until smooth and creamy with no lumps.
Using a cookie scoop or spoon, take a portion of the cookie dough and flatten it slightly. Place about a teaspoon of the cheesecake mixture in the center, then wrap the cookie dough around it, sealing the filling completely.
Place the stuffed cookies on the prepared baking sheet, spaced about 2 inches apart. Bake for 12-15 minutes; the edges should be set while the centers remain soft.
Allow the cookies to cool on the baking sheet for 5 minutes, then transfer them to a wire rack to cool completely.
Notes
For a striking presentation, arrange the cookies on a dark, elegant plate and dust with powdered sugar.