Here’s a recipe from Mrs Beeton from 1859 or so. It’s delicious.
Boil the carrots in milk until tender enough to mash to a pulp; add the remaining ingredients. If needed, add more milk to make the pudding of the consistency of thick batter.
If you want to steam the pudding, put the mixture into a buttered basin, tie it down with a cloth, and steam for 2-1/2 hours: if to be baked, put it into a pie-dish, and bake for about an hour; turn it out of the dish, sift sugar over it, and serve with custard or heavy cream.