Heat the oven to 350°F (175°C) with a rack in the center. Grease a 10 inch bundt pan thoroughly, getting into every ridge and around the center tube, then dust with flour and tap out the excess. Grease it right before the batter goes in.
In a large bowl, whisk the flour, brown sugar, baking powder, baking soda, cinnamon, nutmeg and salt. Break up any brown sugar lumps first, then whisk 20 to 30 seconds.
In a second bowl, whisk the oil, maple syrup, eggs and vanilla until smooth and slightly lighter in color.
Pour the wet mixture into the dry in two or three additions, stirring gently with a spatula after each. Stop as soon as the flour streaks disappear. Scrape the bowl once.
Fold in the grated carrots and chopped pecans until evenly distributed. Blot the carrots with a paper towel first if they look wet.
Spoon the batter evenly around the pan, smooth the top, then tap the pan firmly on the counter two or three times.
Bake 50 to 60 minutes, checking from 45 minutes. A skewer should come out with moist crumbs and no wet batter, or 205 to 208°F (96 to 98°C) in the center. Tent with foil if the top browns too fast.
Cool in the pan 15 to 20 minutes. Run a thin knife around the center tube and outer edge, set a rack on top, flip, and lift the pan away.
Cool completely on the rack, about 1 hour 30 minutes. Do not frost a warm cake.
Stir the frosting until smooth, loosening with 1 to 2 teaspoons (5 to 10 ml) milk or cream if needed. Spoon over the cake and let it run down the ridges. Scatter chopped pecans over while the frosting is still soft.