In a large bowl, whisk together the oil, eggs, and sugar until combined. Add sour cream, sourdough discard, and vanilla, and whisk again until combined.
In a medium bowl, whisk together the flour, baking soda, baking powder, cinnamon, ginger, and salt. Add flour mixture to the liquid ingredients, and stir about 8-10 times to get some of the flour absorbed, but not all. Distribute carrots evenly over the top of the batter and, stir a few times, then add the pecans, and stir again until lightly distributed. You don't want to overmix, you should just barely get the flour streaks to disappear.
Pour into an 8-inch pan and bake at 350 degrees F for 28 to 30 minutes, until toothpick has just moist crumbs attached when you poke through the cake.
Let bars cool completely on a wire rack.
For the frosting, add cream cheese and butter to a medium size bowl. With a hand mixer or spatula, beat well until combined and smooth (I prefer hand mixer). Add maple syrup and salt, beat again until smooth and lightened. Taste and adjust with more salt if needed.) Frost with maple cream cheese frosting and cut into bars. Store bars in refrigerator for up to 4 days.