In a small bowl stir together well the butter and the brown sugar and spread the mixture evenly in a well buttered 9x2-inch round cake pan. Pat the pineapple very dry between several thicknesses of paper towels and arrange it evenly on the sugar mixture.
Preheat the oven to 350°F. Into a bowl sift together the flour, the baking powder, the salt, and the cinnamon. In another bowl with an electric mixer cream the butter with the sugar until the mixture is light and fluffy, add the eggs, 1 at a time, beating well after each addition, and beat in the vanilla. Add the flour mixture alternately in batches with the milk, beginning and ending with the flour mixture and beating well after each addition. Pour the batter into the pan, spreading it evenly and bake the cake in the middle of the oven for 45 to 55 minutes or until a tester comes out clean. Let the cake cool in the pan on a rack for 15 minutes, run a thin knife around the edge, and invert the cake onto a plate. Serve the cake warm or at room temperature with the whipped cream or the ice cream.