Preheat the oven to 350°F (180°C) with the oven racks in the upper and lower thirds of the oven. Lightly grease 2 (6-well) 4-inch bun pans with cooking spray.
Make the cookie dough: In a medium bowl, whisk the flour, baking soda, and salt to combine. In a liquid-measuring cup, whisk the sour cream, egg, and vanilla together to combine.
Using a hand mixer, cream the butter, powdered sugar, and brown sugar in a medium bowl on medium speed until light and fluffy, 3 to 4 minutes. Scrape the base and sides of the bowl well. (You can also do this by hand with a silicone spatula, if you prefer, but the quantity is a bit too small for a standard electric stand mixer.)
Add the sour cream mixture, and mix on medium speed until well combined. Scrape the bowl well. Add the dry ingredients in 2 to 3 additions, mixing on low speed just until it’s incorporated.
To assemble the cookies: In a small bowl, mix the brown sugar and melted butter to combine. Scoop a heaping tablespoon (about 19 grams) of the mixture into each prepared well. Use a small offset spatula (or your hands) to help spread it into an even layer.
Place a pineapple ring into the base of each well. Place a cherry in the center of the pineapple ring, pressing down lightly.
Scoop the cookie dough by 2-tablespoon (about 38 grams) portions, and place on the pineapple. Use a damp hand to gently press the cookie dough flat, covering the pineapple.
Transfer to the oven and bake, swapping pans halfway through, until the cookies are visibly browned around the outer edge, 14 to 17 minutes. Remove the cookies from the oven, and transfer to a wire rack to cool for 5 minutes.
While the cookies cool in the pan, line two baking sheets with parchment paper. After the cooling time, invert the pan(s) in a swift, firm motion, slamming it down onto one of the prepared baking sheets. Use a spatula to transfer the unmolded cookies to the other prepared baking sheet, leaving any excess syrup and juices behind.
Cool the cookies for at least 8 minutes (or completely) before serving. Store in an airtight container for up to 3 days.
