Shake the can of coconut milk vigorously for a few seconds. In a heavy saucepan, bring 1 1/4 cups of the coconut milk, maple syrup, and the salt (just) to a simmer over low heat.

While that is heating, in a separate bowl, whisk together the remaining coconut milk, arrowroot powder, and cocoa powder. It should look like chocolate frosting.

When the coconut milk and sugar mixture has started simmering, take about 1/4 cup of it and whisk it little by little into the arrowroot mixture, creating a slurry. Turn down the heat to the very lowest setting. Now drizzle the arrowroot slurry mixture into the simmering pan of coconut milk, whisking vigorously all the while. Keep whisking until the pudding comes back up barely to a simmer and thickens up a bit, about a minute.

Remove the saucepan from heat, continue whisking while it is cooling for about a minute. Now whisk in the chocolate and vanilla. Keep stirring until the pudding is smooth. Transfer to a bowl and place in the refrigerator to chill thoroughly. To prevent a skin from forming, press plastic wrap up against the surface of the pudding.