Preheat the oven to 350°F (175°C), grease and line a 9x13-inch pan, then whisk together the 2 cups flour, 2 tsp baking soda, 1 1/2 tsp cinnamon, 1/2 tsp nutmeg, and 1/2 tsp salt in a large bowl.

In a separate bowl, whisk the 4 eggs and 1 1/2 cups sugar until pale and slightly thickened, about 2 minutes, then whisk in the 1 cup vegetable oil until glossy and combined.

Stir the 3 cups grated carrots and 1/2 cup drained pineapple into the wet ingredients, fold into the dry ingredients until just combined, then stir in the 1 cup walnuts.

Pour the batter into the prepared pan and bake at 350°F (175°C) for 40 to 45 minutes, until a toothpick in the center comes out clean. Cool completely in the pan, at least 1 hour.

Beat the 16 oz cream cheese and 1/2 cup butter on medium speed until smooth, about 2 minutes, then add the 3 1/2 cups sifted powdered sugar in 3 additions, mix in the 1 1/2 tsp vanilla, and beat 1 more minute until thick and creamy.

Spread the frosting over the cooled cake, scatter chopped walnuts on top, add a few swirls with your spatula, and slice.