Preheat the oven to 350 degrees. In a small bowl mix the sour cream, 4 tablespoons evaporated milk and dark brown sugar, stirring constantly, for 1 to 2 minutes. Cover and refrigerate. In a large bowl, whisk together the eggs, condensed milk, remaining evaporated milk, and vanilla extract, until well incorporated. Add the bread cubes and mix until the bread is coated. Cover and refrigerate for 2 hours, mixing every 30 minutes, until the milk is mostly absorbed. Add the coconut flakes and stir to incorporate. Grease an 8x8x2-inch glass baking dish with butter. Pour the bread mixture into the baking dish. Bake for 35 to 40 minutes or until the center is set and the top is golden brown. Drizzle with the sour cream mixture before serving.