Pina Colada Cake

Ingredients

• 2 cups (250 grams or 8 3/4 ounces) all-purpose flour
• 1 teaspoon baking powder
• 3/4 teaspoon baking soda
• 1/2 teaspoon salt
• 1 stick (113 grams or 4 ounces) unsalted butter, softened
• 1/4 cup light (55 grams or 2 ounces) brown sugar
• 1 tablespoon (15 ml) dark rum
• 2 large eggs, at room temperature
• 1 cup (237 ml) cream of coconut
• 1/2 cup (72 grams or 2 1/2 ounces) finely chopped fresh pineapple (or pineapple from a can, strained, juice reserved)
• 1 to 2 tablespoons rum (optional)
• 2 tablespoons pineapple juice (optional)
• 1 cup (120 grams or 4 ounces) powdered sugar
• pinch of table or fine sea salt
• 1 1/2 to 3 tablespoons pineapple juice