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. 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 marshmallow filling: Put the salt and egg whites in the bowl of an electric mixer fitted with the whisk attachment. Beat on medium speed until foamy. On high speed, gradually add 1/4 cup of the granulated sugar and beat until stiff and shiny.
Meanwhile, combine the corn syrup, 1/2 cup water and the remaining 3/4 cup sugar in a medium saucepan and bring to a boil over medium-high heat. Cook until the mixture reaches the firm-ball stage, about 245 degrees F on a candy thermometer.
Turn on the mixer to medium speed. Slowly pour the hot syrup into the egg whites, then beat on high until the mixture is thick, fluffy and cool, 5 to 7 minutes. Beat in the vanilla. Let cool completely.
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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