The rich, creamy filling can be made up to 3 days ahead and then piped onto fresh, cooled cookies. Bourbon makes the filling lick-the-bowl good, but you can omit the booze for a kid-friendly treat.
Preheat oven to 375°F with oven racks in the top third and bottom third of oven. Beat butter, granulated sugar, and brown sugar with an electric mixer on medium speed until smooth, about 1 minute. Add eggs, 1 at a time, beating on low speed just until incorporated. Add 1 teaspoon of the vanilla, and beat just until combined. Whisk together flour, baking powder, baking soda, cinnamon, and 3/4 teaspoon of the salt, and add to butter mixture alternately with milk, beginning and ending with flour mixture and beating on low speed just until each is incorporated.
Using a 1-inch cookie scoop, drop dough about 3 inches apart onto parchment paper-lined baking sheets. Bake in preheated oven until cookies are just set and beginning to brown, 9 to 11 minutes, switching pans top rack to bottom rack halfway through baking. Transfer to wire racks, and cool cookies on pans 5 minutes. Remove cookies from pans to wire racks, and cool completely, about 30 minutes.
Beat cream cheese on medium speed until fluffy, about 2 minutes, scraping down sides of the bowl as needed. Add bourbon, nutmeg, 1 cup of the powdered sugar, and remaining 1 teaspoon vanilla and 1/4 teaspoon salt; beat until smooth. Beat heavy cream in a small bowl until stiff peaks form; fold into cream cheese mixture. Pipe 1 tablespoon cream cheese filling onto flat side of half of the cookies. Cover with remaining half of cookies, flat side down, and gently press. Sift remaining 1/3 cup powdered sugar evenly onto the "pies."