Coconut-Pineapple Topping: Pour butter into an 8 x 8-inch baking pan, swirling to coat bottom. Sprinkle evenly with brown sugar and coconut. Spread crushed pineapple over coconut mixture.
Cake: Combine 1 cup flour, sugar, undissolved yeast, and salt in a large mixer bowl. Heat milk, water, and butter until very warm (120o to 130oF). Gradually add to flour mixture. Beat 2 minutes at medium speed of electric mixer, scraping bowl occasionally. Add egg, vanilla extract, and 1/2 cup flour; beat 2 minutes at high speed, scraping bowl occasionally. Stir in remaining flour to make a stiff batter. Spoon evenly over prepared topping. Cover; let rise in warm, draft-free place until doubled in size, about 1 hour.
Bake at 375oF for 30 to 35 minutes or until done. Invert and remove from pan; serve warm.