Preheat oven to 350°F. Lightly coat a 9-inch-square baking pan with cooking spray.
Combine 2¼ cups milk, 1 tablespoon orange zest, ¾ cup orange juice, ½ cup yogurt, ¼ cup honey, 2 eggs, 1½ tablespoons vanilla, 1 tablespoon cinnamon, 1½ teaspoons baking powder, ¾ teaspoon ginger and ¾ teaspoon salt in a large bowl; stir until thoroughly combined.
Add 3 cups oats, ¾ cup each raisins, grated carrot and apple and ½ cup each coconut and walnuts; stir until combined.
Transfer to the prepared pan and spread in an even layer.
Bake until the oatmeal is just set in the center and the top is golden brown, 55 to 60 minutes.
Transfer to a wire rack to cool for 5 minutes before serving.
