Preheat the oven to 350℉. Grease and flour a 10-inch Bundt pan, making sure to coat all crevices well.
In a large mixing bowl, whisk together the flour, brown sugar, baking powder, baking soda, cinnamon, nutmeg, and salt until evenly combined. In a separate bowl, whisk together the vegetable oil, maple syrup, eggs, and vanilla extract until smooth.
Pour the wet ingredients into the dry ingredients and mix gently until just combined. Avoid overmixing. Fold in the grated carrots and chopped nuts until evenly distributed throughout the batter.
Transfer the batter to the prepared Bundt pan and smooth the top.
Bake for 50-60 minutes, until a toothpick inserted into the center comes out clean. Let the cake cool in the pan for 15–20 minutes, then carefully invert onto a wire rack to cool completely.
In a mixing bowl, beat the cream cheese and butter together until smooth and creamy. Add the powdered sugar and vanilla extract, then beat until fully combined and fluffy. Beat in the milk, one tablespoon at a time, until the frosting reaches a thick but spoonable consistency.
Once fully cooled, spoon the cream cheese frosting over the top of the cake. Finish with additional chopped nuts. Slice and serve.