Mix cream cheese, powdered sugar, and vanilla until smooth. Scoop small portions onto parchment and freeze until firm. This step is non-negotiable—it prevents leaks.

Cream butter and sugar until light. Add egg and vanilla, then mix in dry ingredients and milk just until combined. The dough should be soft but not sticky.

Flatten a dough portion, place a frozen cheesecake center in the middle, and seal completely. Roll gently to smooth.

Bake until the edges are set and the tops look dry but pale. Overbaking will dry them out.

While still warm, roll cookies in cinnamon sugar so it sticks evenly.