Preheat the oven to 350°F (175°C). Thoroughly spray a 9-inch pie dish with cooking spray and set aside.
In a large microwave-safe bowl, melt the butter (about 1 minute on high). Let it cool briefly so it won’t cook the egg.
Add the egg, packed brown sugar and vanilla to the melted butter and whisk until smooth.
Stir in the flour and salt until just combined; do not overmix.
Pour the batter into the prepared pie dish and smooth the top lightly with a spatula. Bake for 10 to 12 minutes, until the edges have set and the center begins to firm.
Remove the pie from the oven. Evenly sprinkle 3/4 cup chocolate chips over the crust, then evenly distribute the shredded coconut on top.
Drizzle about 10 ounces sweetened condensed milk evenly over the coconut, then drizzle the 4 to 5 ounces of caramel sauce over the top.
Return the pie to the oven and bake for about 25 minutes more, until there is slight bubbling near the edge and the center looks set; watch closely during the last 10 minutes to prevent burning.
Cool the pie in the dish on a wire rack while you melt 3/4 cup chocolate chips in a small microwave-safe bowl, heating in short bursts and stirring until smooth.
Drizzle the melted chocolate over the cooled (or still-warm) pie in long vertical lines using a spoon or a bag with the corner snipped.
Allow the pie to cool completely on a wire rack for at least 4 hours or overnight so the chocolate sets and the filling firms before slicing.