Peel the carrots and rub them on a fine grater. Sprinkle the carrots with sugar in a heavy-bottomed saucepan and set on very slow heat. We do not add water, the carrots will let some juice and this will be enough.
Cook, stirring occasionally until a gruel is formed. It took me 50 minutes. (You can start stewing with a lid, stir more often, and then see how much liquid has formed, whether it is worth keeping it under the lid or evaporating. If necessary, you can add a little water.) At the end of cooking, add grated lemon zest, vanilla, and cognac or rum. Let the mixture cool well.
Then we roll up balls the size of a walnut.
Dip them in sugar and put the carrot candies on a plate. The sweets are ready.