How to Make It
Preheat oven to 375°F. Generously butter a 9-by-13-inch (or other 3-quart) baking dish. Spread coconut flakes on a rimmed baking sheet and bake until golden, about 3 minutes. Remove from oven.
Arrange half of the apple pieces in prepared baking dish. Top with oats, toasted coconut flakes, raisins, 1 cup carrots, and ￼½ cup walnut pieces. Whisk together coconut milk, eggs, cinnamon, salt, orange zest, ¼￼ cup sugar, 2 tablespoons melted butter, 2¼ ￼cups water, and remaining 1 cup carrots in a large bowl.
Pour milk mixture over oat mixture. Using the back of a large spoon, press top of mix- ture, making sure liquid soaks through to bottom of dish. Mix together remaining apple pieces, 1 tablespoon melted butter, and ￼¼ cup sugar. Sprinkle apple mixture and remaining ½￼ cup walnut pieces over oats.
Bake until edges are bubbling and center is set, 30 to 35 minutes. Let cool 5 minutes before serving. If making oatmeal in advance, let cool completely before covering and refrigerating. To reheat, spoon into serving bowls, then add a splash of milk and gently heat in microwave until warmed through.