Preheat the oven to 350°F. Spray a 9-inch cake pan with pan spray.
Open the 1 (20-ounce) can sliced pineapple, drain the slices into a bowl and reserve the juice. Pat the pineapple slices dry with paper towels to remove excess moisture. Measure out ¼ cup of the reserved pineapple juice and set it aside.
In a small bowl, stir together ½ cup brown sugar (packed) and ¼ cup salted butter (melted) until smooth.
Spread the brown sugar and melted butter mixture evenly across the bottom of the prepared 9-inch pan.
Arrange the pineapple slices in a single layer over the brown sugar mixture, covering the bottom and up along the sides as space allows. Place the 12 maraschino cherries in the centers of the pineapple rings and in any gaps between slices.
In a small bowl, whisk together 1 ⅓ cup all-purpose flour, 1 teaspoon baking powder, and ½ teaspoon salt.
In a large bowl, beat ¼ cup unsalted butter (softened) with ½ cup granulated sugar and ¼ cup brown sugar (packed) for 2–3 minutes, until well combined and slightly fluffy.
Add 1 large egg, ¼ cup sour cream, ¼ cup milk, and the reserved ¼ cup pineapple juice to the butter-sugar mixture and beat until just combined.
Add the dry flour mixture to the wet ingredients and mix until just combined; do not overmix.
Spread the batter evenly over the arranged pineapple slices in the pan.
Bake at 350°F for 45–50 minutes, or until the top is golden brown and a toothpick inserted into the center comes out clean.
Let the cake cool in the pan for 10–15 minutes. Run a knife around the edge to loosen, place a plate or cake stand over the pan, invert the pan to release the cake, then lift the pan off.