Preheat your oven to 350°F (175°C). If using a regular cake pan, line the bottom with parchment paper; if using a cast iron skillet, place it on the stovetop over medium heat.
Melt ½ cup butter in the skillet (or saucepan) over medium heat, add the brown sugar, and stir constantly for 2–3 minutes until the mixture bubbles and becomes a smooth, thick caramel. If using a cake pan, pour the caramel in and tilt to coat evenly; let cool 5 minutes.
Pat the drained pineapple rings dry, then arrange one ring in the center of the pan and the remaining rings around it; place a maraschino cherry in the center of each ring and press everything gently into the caramel.
In a medium bowl, whisk together the flour, baking powder, and salt for at least 30 seconds until evenly combined; set aside.
Beat the softened butter with an electric mixer on medium speed for 1–2 minutes, then gradually add the granulated sugar and beat for 3–4 minutes until the mixture is pale, light, and fluffy.
Add the eggs one at a time, beating well after each addition, then mix in the vanilla extract and scrape down the sides of the bowl.
Mix the milk and reserved pineapple juice together, then alternate adding the flour mixture and the milk mixture to the butter mixture in three and two additions respectively, mixing on low just until no flour streaks remain — do not overmix.
Pour the batter over the pineapple, spread evenly to the edges, tap the pan 2–3 times to release air bubbles, and bake on the middle rack for 45–50 minutes until a toothpick inserted in the center comes out with just a few moist crumbs.
Let the cake cool in the pan for exactly 10 minutes, run a thin knife around the edges, then place a large serving plate over the pan and quickly flip them together; let sit 1–2 minutes before lifting the pan away.