Place oven rack in middle position and heat oven to 350 degrees F.

For the topping, melt butter in a 10-inch cast-iron skillet placed in hot oven. When melted, remove skillet from oven, swirl to coat evenly with butter, then spread brown sugar evenly over the butter. Drain pineapple, reserving juice. Pat pineapple slices very dry between several thicknesses of paper towel. Cut pineapple slices in half, reserving one whole slice. Place whole pineapple slice in center of skillet, then arrrange half-slices in spoke fashion around whole slice in center.

To make batter, in a small bowl, sift together flour, baking powder, salt, and cinnamon. In a large bowl with an electric mixer, cream the butter with the sugar until the mixture is light and fluffy, add the eggs, one at a time, beating well after each addition, then beat in the vanilla. Add the flour mixture alternately in batches with the milk and pineapple juice, beginning and ending with the flour mixture, and beating well after each addition.

Spoon, or carefully pour batter over brown-sugar-pineapple topping in bottom of skillet, and spread evenly. Bake until top is golden and toothpick inserted into cake center comes out clean, 45 to 55 minutes. Let cake cool in skillet on a rack for 5 minutes, run a thin knife around edge of cake to loosen from skillet. Place serving platter over skillet, carefully invert cake onto platter. Let stand for 1 minute before carefully lifting skillet off. Replace any pineapple stuck to bottom of skillet, scrape any remaining glaze from skillet onto cake. Cool on platter on a rack. Serve warm or at room temperature.

Cake may be made 1 day ahead and chilled, covered. Bring to room temperature before serving.

Makes one 10-inch cake, for 8 to 10 servings.