Preheat oven to 350 degrees F.
Pour melted butter into a 10 inch cake pan. Swirl butter around to totally cover inside surfaces of pan. Sprinkle sugar and grated ginger over top. Arrange pineapple slices in a single layer and drizzle with lime juice. Set aside.
Sift together the dry ingredients for the batter and set aside. Cream together the butter and sugar until light and fluffy. Add the egg and beat until smooth. Whisk the molasses and buttermilk together in a small bowl.
Alternating, add 1/3 dry ingredients and 1/3 buttermilk mixture to the creamed butter mixture. Beat in between additions. Scrape down the sides and beat for 1 minute to develop structure of cake.
Pour batter over pineapple slices in cake pan. Bake for 40 to 50 minutes. Cake is done when a knife inserted in the centre comes out clean.
Leave cake in pan and cool on a wire rack for 30 minutes. Invert onto a plate and serve.