Preheat oven to 350F. Spray a 9-in. round non-stick cake pan with oil. Line bottom with a piece of parchment. Set pan on a baking sheet. Reserve 1/2 cup cherries. Coarsely chop remaining cherries. Set aside. Melt 3 tbsp butter with brown sugar in a medium frying pan set over mediumhigh. Cook, stirring occasionally, until it comes to a gentle boil, 2 to 3 min. Add pineapple (do not add any juice). Stir until pineapple is just tender, about 3 min. Remove from heat. Add rum and reserved cherries. Pour into prepared cake pan, spreading fruit in a single layer, keeping cherries near the centre. Stir flour with baking powder, salt and ginger in a medium bowl. Beat 1/2 cup butter with 3/4 cup sugar in a large bowl, using an electric mixer on medium-high, for 3 min. Add eggs, 1 at a time, beating well and scraping down side of bowl after each addition. Beat in vanilla. Reduce speed to low and beat in a third of flour mixture, then half of milk. Repeat additions, ending with flour mixture, until well mixed. Add chopped cherries to batter, then spoon batter over pineapplecherry layer. Don’t worry if it doesn’t cover fruit entirely, because batter will spread as it bakes. Bake in centre of oven until cake is puffed and golden brown, about 30 min. Cover with foil, then continue baking until a cake tester inserted into centre of cake comes out clean, 15 more min. Remove cake from oven and let stand in pan for 10 min. Run a knife around edge, then place a large cake plate upsidedown on top of pan and invert cake onto plate. Carefully peel off parchment. Serve warm or at room temperature.