Chill 2 cans of coconut milk in the refrigerator for at least 4 hours.

Empty the contents of the other 2 cans of coconut milk into a saucepan. Add the honey and bring to a rapid simmer, stirring frequently. Simmer for 20-25 minutes, or until the milk is thick enough to coat the back of a spoon. (After about 10 minutes, you'll notice that the milk will start to turn a golden color – that's ok and is exactly what's supposed to happen.) Remove from heat and let cool completely.

Open the 2 cans of chilled coconut milk. The cream should have risen to the top. Carefully scoop the cream into a mixing bowl. (Reserve the water below to use in a smoothie.) With an electric beater, whip the coconut cream until it's light and fluffy, 3-5 minutes.

Add the condensed coconut milk, rum (if using), lemon juice, and lemon zest. Whip another 2-3 minutes.

Transfer to a lidded container and freeze overnight.

You can eat the ice cream straight from the freezer, but because coconut milk solidified when it's cold, it will be pretty hard. For a creamier treat, add the frozen ice cream to a mixing bowl and whip for about 1 minute to soften it up. If it starts to melt, stick it back in the freezer for 10-15 minutes to firm it back up.