Using a juicer, juice one bunch of carrots. Pour the juice into a baking dish or cake pan, large enough that the juice doesn’t sit too high. Put the pan into the freezer. After 20 minutes, start to scrape the juice with a fork. Do this every 20 minutes until the texture is like small ice crystals that are crisp rather than chunky and icy. Mine froze to the right texture after 1 hour.
For the compote, remove the pits from the apricots by gently tearing the fruit in half. Add the pitted apricot halves, sugar, vanilla, lemon zest, lemon juice and water to a medium saucepan and stir gently to combine. Cook the mixture on medium-low heat until the sugar dissolves and the apricots begin to release their juices. Turn the heat up to medium and gently simmer the apricots, stirring occasionally, until they are very soft and beginning to fall apart, but not completely mushy. About 10-15 minutes.