In a medium bowl, beat together the softened cream cheese, powdered sugar, vanilla extract, and a pinch of salt until smooth and creamy.
Line a small baking sheet or plate with parchment paper. Scoop approximately 2 teaspoons of cheesecake filling into individual portions. Freeze for 45–60 minutes, or until firm enough to handle.
In a large mixing bowl, prepare the Miss Jones Baking Co. Pumpkin Bread, Muffin, Cookie & Pancake Mix according to the cookie directions on the package.
Scoop a portion of pumpkin cookie dough and flatten it into a disk. Place one frozen cheesecake filling portion in the center. Carefully fold the cookie dough around the filling, pinching the edges together to completely seal the cheesecake inside. Gently roll into a ball.
Place the stuffed cookies on a parchment-lined baking sheet, spacing them approximately 2–3 inches apart. Bake according to the package's cookie temperature and timing as a starting point, adding time as needed for the larger stuffed cookies. The edges should be set, and the cheesecake filling should reach 160°F in the center.
Allow the cookies to cool on the baking sheet for 10 minutes before transferring them to a wire rack to cool completely.
In a medium bowl, beat the softened cream cheese and butter until smooth. Add the powdered sugar and vanilla extract, then gradually mix in the milk until the glaze reaches a smooth, drizzling consistency.
Drizzle the cream cheese glaze over the cooled pumpkin cookies. Allow the glaze to set slightly before serving.