Prepare the batter: In a blender, combine grated carrot, eggs, brown sugar, white sugar, oil, and vanilla extract. Blend until smooth.
Mix dry ingredients: In a separate bowl, mix flour, baking powder, baking soda, salt, cinnamon, and nutmeg.
Combine wet and dry ingredients: Add the dry ingredients to the wet mixture and blend or mix until just combined.
Add pecans: Toss pecan nuts with a little flour to prevent them from falling and fold them gently into the batter.
Bake the pudding: Line a pudding mold with parchment paper and pour the batter in. Bake in a preheated oven at 180°C (356°F) for about 40 minutes or until a toothpick inserted comes out clean.
Prepare the frosting: Mix cream cheese with powdered sugar and lemon zest until smooth and creamy.
Serve: Allow the pudding to cool, then frost with the lemon cream cheese frosting. Cut into pieces and serve.