In a medium bowl, sift together the cake flour, baking powder, ginger, cinnamon and salt. In another bowl, using a handheld mixer, beat the butter with the brown sugar until fluffy. Beat in the vanilla and lime zest. Add the eggs, 1 at a time, beating well after each addition. Fold in half of the dry ingredients. Fold in the half-and-half and then fold in the remaining dry ingredients. Spoon the batter over the peaches in the cake pan and bake for about 1 hour, or until a tester inserted in the center of the cake comes out clean. Let cool to room temperature, then run a knife around the side and invert the cake onto a plate. Cut into wedges and serve with the Creamy Caramel Sauce.