Preheat your oven to 350°F (180°C).
Grease a 17 × 25 cm oval baking dish or a 15 × 25 cm rectangular baking dish with butter, then lightly sprinkle it with sugar.
In a large bowl or blender, combine the sweetened condensed milk, eggs, coconut milk, and vanilla extract until smooth.
Stir in the shredded coconut by hand until evenly distributed.
Pour the mixture into the prepared baking dish.
Bake for 50–60 minutes, or until the top is lightly golden and the center is set. A knife inserted into the center should come out clean or with just a few moist crumbs, but not liquid.
Let the dessert cool slightly before serving.
