Preheat the oven to 325°F (160°C).
Partially bake the pie crust for 10–12 minutes, then remove it from the oven and set aside to cool.
Combine sugar and cornstarch in a medium saucepan, whisking them together.
Stir in the coconut milk until the mixture is smooth.
Add dollops of butter to the saucepan, allowing it to melt as the mixture heats.
Cook the mixture over medium-high heat, whisking often, until it thickens, which should take 5–10 minutes.
Remove the saucepan from heat and stir in the vanilla extract.
Set the filling aside to cool slightly.
Mix sugar and cinnamon in a small bowl for the topping.
Pour the prepared filling into the pie crust, filling it three-quarters full.
Drizzle melted butter over the top and sprinkle with cinnamon sugar.
Bake the pie for 25 minutes until bubbling but still liquidy.
Remove it from the oven and cool on a rack at room temperature.
Transfer the cooled pie to the refrigerator and chill for about 3 hours or overnight until fully set.