In a small bowl, whisk together the cornstarch and sugar and set aside.
In another small bowl, add eggs and beat well with a fork.
In a medium saucepan, add coconut milk and milk. Cook over medium heat until warm and then add sugar/starch mixture. Whisk vigorously until the sugar and starch are dissolved. Remove the pan from the heat.
Scoop out about 1 cup of the hot milk mixture. Pour a couple tablespoons of the hot milk into the bowl with the eggs. Whisk together. Continue adding just a bit of the hot milk at a time, while mixing, until you have added enough that the eggs are warm, and you have added the full cup of hot milk. Now, pour the warm egg/milk mixture into the pan of mil an whisk together well.
Return the pan to the heat and continue cooking while slowly whisking almost constantly. Bring mixture to a slow boil and boil (while whisking) about 1 minute. the mixture should now be thickened.
Remove the pan from the heat and whisk in vanilla and coconut extract.
Allow to cool a few minutes (string occasionally), then lay a piece of plastic wrap or parchment paper directly on the surface of the pudding to prevent a skin from forming. Move to the fridge and chill at least 4 hours (and up to 3 days).