Preheat your oven to 350°F and line or grease a loaf pan.
In a large bowl, whisk together the eggs, oil, milk, and vanilla until smooth. Add in the flour, baking powder, baking soda, sugar, cinnamon, and orange zest. Mix until just combined.
Fold in the coconut, pecans, and shredded carrots. Stir everything together until well mixed.
Pour the batter into your prepared pan. Make a line down the center of the batter to help it rise evenly and create a nice crack on top. Bake for about 45 minutes, or until a toothpick inserted in the center comes out clean. Let it cool completely.
For the frosting: Beat the softened cream cheese until smooth. Add confectioners' sugar and vanilla, and mix until fluffy. If needed, add 1–2 tbsp of milk or cream to loosen it up. Spread over the cooled cake.
