Preheat oven to 350 degrees F (175 degrees C). Grease a 9x13-inch baking pan. Pour boiling water over oats in a bowl and let stand until softened, about 10 minutes.

Beat 1/2 cup butter, white sugar, and brown sugar in a large bowl with an electric mixer on medium speed until light and fluffy, about 3 minutes. Add eggs one at a time, beating well after each addition.

Whisk flour, baking soda, salt, cinnamon, and nutmeg in a separate bowl until combined; add to butter mixture and mix until just blended. Stir softened oats and 1 teaspoon vanilla into batter until evenly combined.

Pour batter into prepared pan and spread evenly. Bake in the preheated oven until a toothpick inserted in the center comes out clean, about 35 to 40 minutes. Preheat the broiler.

To make the topping: Combine melted butter, brown sugar, evaporated milk, coconut, walnuts, and 1 teaspoon vanilla in a bowl and stir until blended.

Pour topping over hot cake, spreading evenly.

Broil cake under preheated broiler (about 6 inches from the heat source) until topping is bubbling and lightly browned, about 5 to 10 minutes. Serve warm for a gooey texture or let cool.