Preheat oven to 350°F (180°C). Line baking sheets with parchment paper.
In the bowl of a stand mixer fitted with paddle attachment, beat softened butter and ¾ cup (165 grams) brown sugar at medium speed until creamy, 3 to 4 minutes, stopping to scrape bottom and sides of bowl. Beat in egg until combined.
In a medium bowl, whisk together flour, 1 tablespoon (6 grams) cinnamon, baking soda, baking powder, and salt. With mixer on low speed, gradually add flour mixture to butter mixture alternately with milk, beginning and ending with flour mixture, beating just until combined after each addition and stopping to scrape bottom and sides of bowl. (Batter will be thick.)
Using a 3-tablespoon spring-loaded scoop, scoop batter (about 50 grams each), and place 2 inches apart on prepared pans.
Bake until bottom edges are lightly browned and tops are dry, about 15 minutes, rotating pans halfway through baking. Let cool completely on pans on wire racks.
In a shallow dish, whisk together remaining ½ cup (110 grams) brown sugar and remaining 1 tablespoon (6 grams) cinnamon. Lightly brush melted butter on top and edges of each cookie. Place cookies, top side down, in sugar mixture to coat. (Sprinkle any remaining sugar mixture on tops as needed to evenly coat.)
Spread or pipe Cream Cheese Buttercream onto flat side of half of cookies. Place remaining cookies, flat side down, onto buttercream. Refrigerate in an airtight container for up to 5 days.