Preheat oven to 350F. Grease a 9-inch cake tin with some cooking spray and line the bottom with some parchment paper.
Whisk vegetable oil, lemon juice, vanilla extract, flax eggs, and flex eggs in a bowl.
Add carrots and stir to combine.
Fold in flour, cinnamon, baking soda, and baking powder.
Finally, add chopped nuts and stir to combine.
Transfer the batter to the cake tin and smooth the top.
Bake the cake for 35 minutes or until an inserted toothpick comes out clean.
Cool the cake completely before removing from the tin.