In a large bowl, mix the flour, starter, milk, and coconut oil. Cover and let ferment in a warm area for 6-8 hours.
Preheat oven to 425°F and line your muffin tins with 12 paper liners. Whisk the egg in a small bowl, then add the sugar, spices, and vanilla. Mix well.
Add the egg mixture to the fermented batter and mix until combined.
Sift in the baking soda, baking powder, and salt, and mix until combined. Fold in the carrots and raisins (if using). Don’t over-mix.
Fill the muffin tins evenly with the batter. Bake at 425°F for 5 minutes, then lower to 350°F and bake 12-15 minutes or until a toothpick comes out clean. Cool completely before frosting.
Whisk all the cream cheese frosting ingredients with a hand mixer until smooth, then frost the cooled muffins. Sprinkle with walnuts if desired.