Shake the cans of coconut milk well before opening. Measure ½ cup and set this aside.
Pour the remaining coconut milk into a 2-quart saucepan.
Add the monk fruit, honey and salt.
Warm the coconut milk over medium-low heat, whisking occasionally, until the monk fruit/honey have completely dissolved into the coconut milk, 1 to 2 minutes.
Add the arrowroot to the reserved ½ cup coconut milk and whisk until the starch is totally dissolved.
Pour the cornstarch mixture into the warm coconut milk while whisking gently.
Increase the heat to medium, stirring occasionally - continue cooking the base until it has thickened enough to coat the back of a spoon, 6 to 8 minutes. Do not allow the base come to a boil.
Remove the base from heat and stir in the vanilla.
Pour the base into a shallow container. Let the base cool slightly on the counter so it's not hot when you put it in the refrigerator. Cover the container and refrigerate for at least 4 hours, up to 3 days.
When chilled enough, the base should be slightly pudding-like in texture. Pour the base into your ice cream machine and begin churning.
Churn the ice cream until it thickens considerably and is roughly the consistency of soft-serve ice cream. Depending on your machine, this could take anywhere from 10 to 20 minutes — keep an eye on it!
Scrape the ice cream into your freezer container. Press a piece of parchment or wax paper against the surface to prevent ice crystals from forming. Seal the container.
Freeze for at least 4 hours to harden the ice cream.
If your ice cream is too hard to scoop, let it warm a few minutes on the counter before scooping. I find that coconut ice cream melts a little more quickly than milk-based ice creams, so don't wait too long!