In a large mixer fitted with the whisk attachment, combine the eggs, milk, and oil. Beat in the sugar until fully combined - about 60 seconds. Mix in the vanilla and coconut extract. Set aside.
In a separate bowl, sift the flour, baking soda, cinnamon, nutmeg, and salt. Add the flour mixture to the mixer with wet ingredients and mix until just combined and all flour pockets are gone - do not overmix. Fold in the finely shredded carrots. Pour into prepared springform pan.
Bake cake for 40-45 minutes, until toothpick inserted in the center comes out with a few moist crumbs. Allow cake to cool completely before frosting.