Preheat the oven to 350 F. Line a 9 x 13-inch baking pan with parchment paper.
In a stand mixer fitted with a paddle attachment, combine the sugar, oil, eggs and vanilla extract. Mix on medium-low speed for 2 minutes until light yellow and slightly thickened.
Add the sourdough starter; mix to combine.
In a separate bowl, sift together the 2 cups of flour, chai spice, baking soda, and salt. Gradually add the dry ingredients to the wet mixture; mix on low speed.
Wash, peel, and grate the carrots with a box grater. Combine the carrots with 1 tablespoon of flour; mix well. Add the carrots to the batter and fold in with a rubber spatula.
Pour the batter into the prepared baking pan. You can cover and chill overnight or proceed to bake.
Bake the cake on the center rack for 40 to 50 minutes, or until a toothpick comes out clean when inserted.
Cool in the pan for 15 minutes. Remove to a wire rack and cool completely before frosting the cake.
For the Frosting: In a stand mixer fitted with the paddle attachment, add the softened mascarpone and cream cheese. Sift the powdered sugar directly over the bowl. Add the salt. Mix on medium-low speed until wonderfully light and creamy.
To serve: decorate with pastel chocolate eggs, if using. Cut into square and enjoy!
