Preheat the oven to 375 degrees. Using an electric mixer, beat butter, confectioners' sugar, and 1 teaspoon salt until light. Beat in 2 cups flour until it forms a mass. Transfer to a 9-by-13-inch pan. Place a sheet of plastic wrap on the dough and use it to press the dough into the pan (this will make it easier and will prevent the dough from sticking to your fingers). Bake 20 to 25 minutes or until edges are golden.
Meanwhile, whisk together remaining 2 tablespoons flour, remaining teaspoon salt, and baking powder. Using an electric mixer, beat eggs, brown sugar, and corn syrup until light. Fold flour mixture into egg mixture, then pecans and coconut.
Pour over crust and bake 20 to 25 minutes until set. Run a metal spatula around the edges while still warm, then transfer to a wire rack and cool in pan before cutting into 24 bars.