Preheat the oven to 350°F. Line a 9x9-inch baking pan with parchment paper.
Grate the carrots using a fine grater and add to a large bowl.
Melt the butter, you can do this in the microwave or in a small pot over the stove.
Add the melted butter, cane sugar, eggs, and sourdough discard and mix on low until combined.
Add in the white whole wheat flour, rye flour, baking powder, salt, cinnamon, and cloves.
Mix on low until combined.
Add in the coffee creamer and slowly mix it in until you have a smooth batter.
Transfer to the prepared baking pan and spread it out evenly.
Bake for 30 to 35 minutes, or until a toothpick inserted in the center comes out clean. Allow to cool completely in the cake pan.
To make the frosting: In the bowl of stand mixer fitted with the paddle attachment, add the butter, cream cheese, powdered sugar, and vanilla extract. Mix on low until combined, then speed mixer up to high and mix for 2 to 3 minutes or until light and fluffy.
Reserve about ⅓ cup frosting and add one-third of it into a small bowl and the other two-thirds into another small bowl. Add the matcha powder into the bowl with less frosting and the orange carrot powder into the small bowl with more frosting. Mix up the colors to combine them completely. You can use more or less food color for a brighter color if you want.
Transfer the green frosting to a piping bag with Ateco tip #68 and the orange frosting to a piping bag with Ateco #6.
Add the remaining white frosting onto the carrot cake and spread it out evenly.
Using the orange frosting, pipe a line the size of the carrot you’d like to pipe and zig zag the frosting back and forth while making the line shorter each time so it creates a triangle.
Using the green frosting with the tip vertical (not horizontal as you’ll get a petal) pipe 2 to 3 small stems.
Continue adding carrots on the cake in a freeform way!