9 tablespoons unsalted butter (1 stick + 1 tablespoon, softened, plus more for buttering ramekins)
1/2 small fresh pineapple (peeled, cored and cut into 1/3-inch cubes, about 1-1/2 cups)
1/2 cup light brown sugar
2/3 cup granulated (white) sugar
3 large eggs
1 teaspoon pure vanilla extract
1 cup plus 3 tablespoons unbleached all-purpose flour
1 teaspoon baking powder
1/8 teaspoon salt