Turn on the oven to 400 degrees. Scoop the butter into a large, microwave-safe bowl and melt in the microwave at 50% power for 1 minute. Scoop the bread into the bowl and stir slowly until it is evenly coated. Spread the bread on a rimmed baking sheet, slide it into the oven and toast, stirring every 5 minutes, until it is richly browned, about 15 minutes. Remove the bread and turn the oven down to 300 degrees. Butter an 8-inch-square baking dish and scoop the bread into it.
In a medium bowl, whisk together the eggs, vanilla and salt. In a small (1- to 2-quart) saucepan, heat the coconut milk and the granulated sugar over medium-low, stirring until the mixture is just warm (not close to boiling) and the sugar is dissolved. Pour the warm coconut milk into the eggs in a slow stream, whisking constantly, until well combined. Pour the custard over the bread. Let the bread soak up the custard for 15 minutes, gently stirring the mixture every few minutes. Slide the baking dish into the oven and bake until the bread pudding is barely set at the center, about 30 minutes. Sprinkle with confectioners' sugar, cut into pieces, place them on small plates and you're ready to delight a few friends.
Variations: Garnish the finished bread pudding with about 1/4 cup chopped fresh basil and 1 cup chopped papaya. Serve with crema.