When does the ‘Carrot Fast’ begin?
To understand the origin of this expression, we need to explain what the ‘Zagovenye’ or ‘Fast’ actually is. In Orthodoxy, it refers to the day before the start of Lent, when believers are still allowed to eat meat, milk and other foods. Afterward, they fast, meaning they abstain from so-called "fast foods" (animal-derived products).
Carrots are not among these. Vegetables are allowed during Lent, with the possible exception of those days when believers abstain from food altogether. And since there is no ‘Carrot Fast’, there's no point in expecting the promised answer. This is where this humorous expression originated from. In a similar situation, you could also say: "When the crayfish whistles on the mountain."
Some English equivalents would be: “When pigs fly,” “when hell freezes over,” “on the 30th of February.”