Preheat oven to 375F. Set rack to middle position. Prepare 13x9 pan with nonstick baking spray.
In a large bowl, add pureed carrots, sugar, oil, eggs, and vanilla. Whisk together until evenly mixed.
In a medium bowl, sift together flour, baking powder, baking soda, salt, cinnamon, cloves, and nutmeg.
Stir the dry ingredients into the wet ingredients and add shredded carrots and walnuts, if using.
For Cream Cheese Layer
In a medium bowl, mix together cream cheese and sugar with hand mixer or whisk.
Add in egg and vanilla and mix until smooth.
Assemble
Pour ¾ of carrot bar batter into prepared 13x9 baking pan.
Using offset spatula, spread thin cream cheese layer on top of carrot batter until no batter is showing through. Spoon remaining carrot batter into dollops randomly over cream cheese layer.
Swirl with butter knife the two layers together, creating a pretty swirl pattern.
Bake until toothpick inserted into center comes out clean, about 35-40 minutes.
Remove from oven and allow to cool for 20 minutes in pan. Serve warm or room temperature.
Video
Notes
These should be popped in the fridge with the cream cheese swirl at 2-3 days. You can also freeze. Just wrap really well in plastic wrap.