Preheat oven to 350°F (175°C). Line two 9-in (23cm) round cake pans with parchment paper and coat with a cooking spray.
In a large skillet, toast the pecans over medium heat for about 5 minutes, stirring frequently to prevent burning. Nuts should be fragrant and lightly toasted.
Cool the toasted pecans and very coarsely chop them, reserving about 1/2 cup for decorating the top, if desired.
In a medium bowl, whisk together flour, baking powder, cinnamon, salt and nutmeg. Set aside.
In a mixing bowl with paddle attachment, beat the eggs, vegetable oil, sugar and vanilla extract until combined, about 2 minutes.
Add the dry ingredients and mix until mostly combined with some dry flour visible.
Add shredded carrots and walnuts. Mix the batter with a spatula until everything is just combined.
Divide the batter into the prepared pans. And bake for 23-25 minutes, or until the inserted toothpick comes out clean.
Cool the cakes on a wire rack for 5 minutes. Then remove the cakes from the pan and cool completely.