Set the oven to 350°F and cover 2 baking sheets with parchment paper. The parchment creates a lined surface for shaping and baking the cookie cups.

Beat the butter in the mixer until creamy, then blend in the cookie-dough cream cheese. Continue until the mixture looks uniform, without visible cream cheese pieces.

Beat both sugars into the butter mixture for about 1 minute, then scrape the bowl and incorporate the egg and vanilla. The mixture should look evenly blended, with no unmixed butter along the bowl walls.

Whisk the flour, cornstarch, baking powder, baking soda, and salt together in another bowl, keeping both graham crust portions separate. Even distribution helps the cookies rise consistently.

Add the flour mixture to the mixer, stop when about half has blended in, then use a wooden spoon to fold in the crust chunks and finish combining the dough. Stop once no dry flour remains, leaving recognizable graham pieces throughout.

Portion 8 to 10 cookies with a large scoop, shape each into a ball, coat with crushed graham crust, and arrange 4 on each baking sheet. The coating should cling to the surface, with open space between the dough balls.

Press a tablespoon into each center, bake for 10 minutes, then immediately deepen the wells with a small glass or measuring cup and leave the cookies to cool completely. The edges should look matte and set while the warm centers remain pliable enough to reshape.

Beat the filling cream cheese until smooth, then blend in the sour cream, condensed milk, lime zest, and lime juice, reserving the wedges and whipped cream for topping. The filling should look creamy and uniform, without cream cheese lumps.

Spoon the filling into the completely cooled cookie wells and refrigerate for 2 hours. The chilled centers should become thicker and hold their shape better.

Finish each chilled cookie with piped whipped cream and a lime wedge. The cream should sit neatly on the filling rather than sinking into a warm center.