Preheat the oven to 350°F. Lightly coat a 9x13-inch cake pan with baking spray (the kind with flour) and set aside.
In a large mixing bowl, beat 4 large eggs, 1 1/4 cups vegetable oil, 1 cup white sugar, 1 cup brown sugar, and 3 teaspoons vanilla extract together until the mixture is lighter in color and combined.
In a separate bowl, whisk together 2 cups all-purpose flour, 2 teaspoons baking soda, 2 teaspoons baking powder, 3 teaspoons ground cinnamon, 1/2 teaspoon salt, and 1/4 teaspoon ground nutmeg until evenly distributed.
Add the dry ingredients to the wet ingredients and mix until just combined and there are no large dry streaks, about 2 to 3 minutes.
Stir in 3 cups grated carrots and 1 cup crushed pineapple (drained) until evenly incorporated.
Fold in 1 cup chopped pecans gently, keeping the batter evenly mixed without overworking it.
Pour the batter into the prepared 9x13-inch pan and smooth the top. Bake for 40 to 50 minutes, or until a toothpick inserted in the center comes out clean or with only a few moist crumbs.
Remove the cake from the oven and let it cool completely in the pan on a wire rack before frosting.
To make the frosting: in a large bowl beat 1/2 cup softened butter and 8 oz. softened cream cheese until smooth and fluffy. Add 4 cups powdered sugar and 1 teaspoon vanilla extract, then beat until the frosting is smooth and spreadable.
Spread the frosting evenly over the cooled cake. Sprinkle with extra chopped pecans if desired. Slice and serve.