In a large saucepan bring the water to boiling. Add oats and 1/4 cup butter. Reduce heat to low; cook for 5 minutes to soften the oats, stirring occasionally. Remove from heat; set aside.
In a large bowl stir together egg and the 3/4 cup brown sugar; set aside. In a medium bowl stir together the whole wheat flour, all-purpose flour, baking soda, cinnamon, salt and nutmeg. Using a wooden spoon, stir oat mixture into egg mixture until combined. Fold in flour mixture just until moistened. (Batter will be thick.)
Spread batter into a lightly greased 2-qt. rectangular baking dish. Bake in a preheated 350º oven for 30 to 35 minutes or until a wooden toothpick inserted near the center comes out clean. Remove to a wire rack. Preheat broiler.
Meanwhile, in a medium saucepan melt 1/4 cup butter. Stir in the 3/4 cup brown sugar and the half-and-half until combined. Remove from heat. Stir in coconut, pecans, and vanilla; mix well. Spoon coconut mixture over hot cake.
Broil 4 to 5 inches from the heat for 3 to 4 minutes or until topping is bubbly and begins to brown. (Watch closely.) Cool in pan on a wire rack at least 30 minutes before serving. Serve warm or at room temperature.