Preheat the oven to 300°F (150°C). Spread the pecans on a baking sheet and bake for 7-8 minutes. Then remove from the oven and set aside.
Preheat the oven to 350°F (175°C).
In a large mixing bowl, whisk the flour, baking powder, baking soda, salt, cinnamon, ginger, and nutmeg to combine. Set aside.
In another large mixing bowl, whisk the eggs, oil, brown sugar, sugar, and vanilla to combine. Then add the dry ingredients and whisk just until combined. Add grated carrots and 1 cup (110g) of toasted pecans and fold into the batter. Set aside.
Line a 9x13 inch (23x33cm) baking pan with parchment paper with an overhang around the sides. Spray a bit of non-stick spray underneath the paper that it sticks to the pan. Fill the cake batter into the pan and spread evenly. Bake for 40-45 minutes or until a toothpick inserted into the center comes out clean. Cover the cake loosely with foil after 20-30 minutes to prevent heavy browning, if necessary. Remove the cake from the oven and let cool for about 15 minutes. Then lift it out of the pan and transfer to a wire rack and let cool completely.
In a large mixing bowl, using an electric mixer fitted with a whisk attachment, mix the butter on medium-high speed until soft and creamy, for about 2 minutes. Then add the cream cheese and mix until soft, combined, and no lumps remain, for about 2 minutes. Add the powdered sugar and vanilla and mix until creamy, about 1-2 minutes.
Spread the frosting on top of the cooled cake and sprinkle with the remaining 1 cup (110g) of toasted pecans. Serve immediately or store in an airtight container in the fridge for up to 4 days. Freeze for up to 3 months.