Preheat the oven to 350F degrees.
Line a 13x9 inch baking pan with parchment paper so that the paper extends up the sides of the pan.
In a medium mixing bowl, whisk together 2 cups of the flour and 1 cup of the brown sugar. In a small microwave safe bowl, melt the butter in the microwave. Stir the melted butter into the flour mixture until well combined.
Press the crust mixture into the bottom of the parchment paper lined baking pan. Bake at 350F for 12-15 minutes until lightly browned. Remove from the oven and cool for 10 minutes.
Reduce the oven temperature to 325F degrees.
In a large bowl whisk together the remaining ½ cup of flour, ¼ cup of the brown sugar, 3 eggs, 1 can of sweetened condensed milk, and the vanilla extract. Melt the remaining ¼ cup of butter in the microwave in a microwave safe bowl, then stir into the filling mixture.
Add the semisweet chocolate chips and 3 cups of the shredded coconut; stir well.
Pour the filling mixture over the baked crust. Sprinkle the top with the remaining 1 cup of coconut.
Bake the coconut bars as 325F for 30 minutes, until golden brown on top.
Cool the bars in the pan for 10 minutes, then carefully remove from the pan by lifting the sides of the parchment paper and moving the bars to a cooling rack. Cool completely to room temperature, then cut into bars and serve.