Prepare a large baking sheet by lining it with parchment paper and keep it aside. In a sizable saucepan over medium heat, combine the light brown sugar, granulated sugar, evaporated milk, light corn syrup, and salted butter, stirring frequently until the mixture becomes fully melted and uniform. Let the mixture come to a boil and continue boiling undisturbed until it reaches the soft ball stage at 235°F, which typically takes 3 to 5 minutes. Once it hits the required temperature, take the pan off the heat and gradually blend in the vanilla extract. Fold in the chopped pecans and flaked coconut, then stir continuously for 4 to 5 minutes, allowing the mixture to thicken and cool slightly. With a medium (2-tablespoon) cookie scoop, portion the mixture onto the prepared baking sheet. Sprinkle each cookie with flaked sea salt and allow them to set fully, either at room temperature or by placing the tray in the refrigerator.