Instructions

Adjust oven rack to middle position and heat oven to 350 degrees. Grease 9-inch round cake pan, line with parchment paper, and grease parchment.
Cut seven ½-inch-thick crosswise slices from pineapple. (Reserve remaining pineapple for another use.) Using 3¼-inch round cutter, cut slices into neat rounds; discard trimmings. Using 1¼-inch round cutter or apple corer, remove core from pineapple slices to create rings; discard core pieces.
Combine brown sugar and 1 cup pineapple juice in 12-inch skillet. Add pineapple rings to skillet in single layer. Bring to boil over medium-high heat and cook until rings have softened, about 10 minutes, flipping rings halfway through cooking. Transfer rings to prepared pan, placing 1 ring in center of pan and arranging remaining 6 rings around circumference of pan (rings will fit snugly in pan without overlapping). Place cherries in centers of rings.
Return brown sugar mixture to boil over medium-high heat and cook, stirring frequently, until rubber spatula dragged across bottom of skillet leaves trail that fills in slowly, bubbles increase in size, and mixture registers 260 degrees, 3 to 6 minutes. Carefully stir in 12 tablespoons butter and ½ teaspoon salt until butter is melted (caramel may look separated at first). Return mixture to boil and cook until frothy and uniform in texture, about 1 minute. Let caramel cool off heat for 5 minutes.
Transfer caramel to 4-cup liquid measuring cup. Pour ¾ cup caramel evenly over pineapple rings, gently shaking pan to distribute. Whisk rum and remaining 2 tablespoons pineapple juice into remaining caramel; set aside.
Whisk flour, baking powder, and remaining ½ teaspoon salt together in bowl. Whisk granulated sugar, milk, eggs, and vanilla in large bowl until smooth, about 1 minute. Whisk 8 tablespoons melted butter into milk mixture until combined. Whisk flour mixture into milk mixture until no dry flour remains.
Transfer batter to prepared pan and smooth top with rubber spatula. Bake until light golden brown and toothpick inserted in center comes out clean, 50 minutes to 1 hour.
Transfer pan to wire rack. Immediately run paring knife between cake and sides of pan. Using toothpick, poke about 80 holes evenly over cake. Microwave reserved caramel mixture until warm, about 1 minute. Brush cake with ½ cup reserved caramel mixture. Let cake cool in pan for 25 minutes. Carefully invert cake onto serving plate. Brush top of cake with remaining reserved caramel mixture as desired. Serve warm or at room temperature, passing any remaining caramel mixture separately.