Preheat the oven to 350°F (175°C). Place a rack in the center of the oven. Grease a 10 inch bundt pan very well, making sure to get into all the ridges, then dust it lightly with flour and tap out the excess.

In a large mixing bowl, combine the flour, brown sugar, baking powder, baking soda, cinnamon, nutmeg, and salt. Break up any brown sugar lumps with your fingers or a spoon, then whisk well so everything is evenly mixed.

In a separate bowl, whisk together the vegetable oil, maple syrup, eggs, and vanilla extract until smooth and slightly lighter in color. If the eggs were very cold, you can warm them in a bowl of warm water for a few minutes before cracking.

Pour the wet ingredients into the dry ingredients in two or three additions, gently stirring with a spatula after each addition. Scrape the bottom and sides of the bowl once, then stop mixing as soon as no dry flour remains. A few small lumps are fine.

Fold in the grated carrots and chopped walnuts or pecans until they are evenly distributed. If the carrots seem very wet, gently blot them with a paper towel before adding. For extra flavor, you can toast the nuts briefly in a dry pan and let them cool before chopping.

Spoon the batter evenly into the prepared bundt pan. Smooth the top with a spatula, then tap the pan firmly on the counter a couple of times to release any air bubbles.

Bake at 350°F (175°C) for 50 to 60 minutes. Start checking around 45 to 50 minutes. The cake is done when a skewer or toothpick inserted into the center comes out with a few moist crumbs but no wet batter. If you use an instant read thermometer, the center should be around 96 to 98°C.

Place the pan on a wire rack and let the cake cool in the pan for 15 to 20 minutes. Run a thin knife or small offset spatula around the center tube and outer edge. Place a rack on top, flip the pan and rack together, then gently lift the pan off. Let the cake cool completely.

Transfer the cooled cake to a serving plate. Scoop the cream cheese frosting into a bowl and stir until smooth and spreadable. If it seems very thick, add 1 to 2 teaspoons of milk or cream and stir again. Spoon the frosting over the top of the cake, nudging it so it drips down the sides. Sprinkle extra chopped nuts on top while the frosting is still soft.