Reduce to a simmer and cook for 20-30 minutes, or until carrots are very soft.
Purée the soup until creamy. Set aside and keep warm.
Place the butter in a clean 10-inch Lodge Cast Iron Skillet and cook over low heat until melted. Add the flour and cook for 3 minutes, while stirring, making a blonde roux. Deglaze the pan with the carrot soup while stirring constantly. Return all the soup to the 5-quart Lodge Dutch Oven.
In a separate medium/small bowl, blend together half-and-half and egg yolks very well.
Temper the egg yolk mixture with the hot carrot soup.
Remove from heat, adjust seasoning if needed, and ladle into warm bowls immediately.
For the carrot ribbons:
Blanch carrot peels in boiling water, then remove and pat dry.
Bring 2 cups of frying oil in a 10-inch Lodge Cast Iron Skillet between 350-375°F. Fry carrot ribbons in batches until translucent in color and crispy in texture. Remove with a slotted spoon and place onto paper towel to drain any excess fat.