In a bowl, beat eggs, brown and white sugar together for 2 minutes. Then, add canola oil and olive oil and mix well. Gradually add flour and mix until just combined. Next, fold in grated carrots, chopped pecans, cinnamon, and nutmeg until a uniform mixture is obtained.
Pour the cake batter into a greased rectangular pan and place it in a preheated oven at 350°F (175°C) using the turbo setting for about 45-55 minutes, or until a toothpick inserted into the center comes out with moist crumbs. Remove the cake from the oven and allow it to cool completely outside of the oven.
Melt the butter in the microwave and add powdered sugar, mixing until well combined. Then, add the cream cheese and continue mixing until fully incorporated.
In a separate mixing bowl, whip the heavy cream until stiff peaks form. Gently fold in the cream cheese mixture until a stable frosting is obtained.
Once the cake has cooled, spread a layer of frosting on top using a palette knife, then sprinkle chopped pecans and cinnamon over the frosting.
