Heat the oven to 175 C / 350 F. Grease a 9-inch cast iron skillet or round cake pan.

Melt the butter in the pan over low heat, then sprinkle the brown sugar evenly over it. Stir until it starts to dissolve into a smooth caramel, about 2 minutes, then remove from heat.

Arrange the pineapple rings over the caramel in a single layer, tucking a cherry into the center of each ring and filling any gaps with extra cherries.

Whisk the flour, baking powder, and salt together in a bowl and set aside.

Beat the softened butter and sugar together until light and fluffy, about 3 minutes. Add the eggs one at a time, then the vanilla, beating well after each addition.

Alternate adding the flour mixture and coconut milk to the butter mixture in three additions, mixing just until combined. Fold in the shredded coconut and reserved pineapple juice by hand.

Pour the batter over the arranged fruit and spread it evenly with an offset spatula. Tap the pan twice on the counter to release air bubbles.

Bake for 35 to 40 minutes, until a toothpick inserted in the center comes out clean and the top springs back when pressed. Internal temperature should read about 200 F / 93 C.

Cool the cake in the pan on a wire rack for 15 minutes, no longer. Run a knife around the edge, place a plate over the pan, and invert quickly and confidently.

Lift the pan away carefully, the caramel and rim will be hot. Let the cake cool another 10 minutes before slicing.