Preheat your oven to 350 degrees Fahrenheit.
Grease and line an 8" round pan with parchment paper.
In a large bowl, whisk together flour, sugar, spices, baking soda, and salt.
In a small bowl, whisk oil, egg, milk, lemon, yogurt, and vanilla.
Pour the wet mixture into the dry mixture and fold with a spatula to combine (the batter will be very thick at this point).
Fold the shredded carrots and into the batter.
Transfer the batter to the prepared pan and bake for 22-25 minutes or until a toothpick inserted comes out with a few moist crumbs.
For the frosting, cream together the butter, cream cheese, vanilla, and salt.
Add the powdered sugar in two additions, mixing until smooth.
Add milk as needed to reach a smooth frosting consistency.
Run an offset spatula around the sides of the baked cake to release it from the pan.
Add the frosting on top of the cooled cake.
Spread with a spoon or offset spatula.
Sprinkle with cinnamon if you'd like.
Slice and enjoy!
Store any extra in the fridge.
