For the cookies: Line 2 baking sheets with parchment paper and lightly coat with cooking spray.
Whisk together the flour, baking soda, baking powder and salt in a medium bowl. Mix in the cinnamon. Beat together the granulated sugar, butter and vanilla in a large bowl with an electric mixer on medium-high speed until light and fluffy. Add the egg and beat until combined. Reduce the speed to low and add the flour mixture in 3 batches, alternating with the buttermilk in 2 batches, beating after each addition until just combined.
Scoop 2-tablespoon mounds of batter onto the baking sheets about 2 inches apart. Moisten your fingers and gently form each mound into a round and slightly smooth the top. Refrigerate until firm, about 30 minutes.
Preheat the oven to 400 degrees F.
Bake, rotating the trays halfway through, until the tops of the cookies bounce back when gently touched, 10 to 12 minutes. Cool on the baking sheets 5 minutes, then transfer to a rack to cool completely.
For the buttercream filling: Put the butter in the bowl of an electric mixer fitted with the paddle attachment and beat on medium speed until fluffy. Gradually add half of the confectioners' sugar, beating. Beat in the milk 1 tablespoon at a time, then add the remaining confectioners' sugar and beat until incorporated, smooth and creamy, scraping the bowl as needed, about 3 minutes. Mix in the vanilla. Beat in the dulce de leche until smooth.
To assemble the whoopie pies, flip half of the cookies over on a work surface and spread them with the filling. Top each with another cookie, bottom facing in, to make a sandwich.
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