Add coconut milk and cornstarch/arrowroot to a saucepan and whisk to combine.
Cook over medium heat until bubbly and thickened (approximately 5 minutes, but may be less).
Remove the pan from the heat and stir in the maple syrup, peanut butter, vanilla, and a pinch of salt. Taste and adjust flavor as needed (realizing that when it's cool, the flavors will pop a bit more)...you may need to adding more maple syrup for sweetness, salt, or peanut butter.
Pour the mixture into a heat-proof glass container and let cool on the countertop for 10 minutes. Then cover the pudding with plastic wrap or parchment paper so that it touches the surface of the pudding completely (to prevent a film). See photos if this doesn't make sense.
Chill for at least a few hours before eating, or ideally overnight.
Serve as-is or topped with coconut whipped cream, crushed peanuts, or cacao nibs. It would also work well as a pie filling! Leftovers should last in the fridge for up to 5 days.