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Preheat the oven to 350°F. Grease a 9" x 13" pan. For easiest removal, line the pan with parchment, and grease the parchment.
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To make the crust: In a medium-sized bowl, beat the butter, sugar, and salt until light and fluffy.
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Add the flour, stirring until just combined.
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Pat the mixture into the prepared pan. Lightly flour your fingers as you press the dough into the pan; it's sticky, and will cover the bottom of the pan with only a thin layer.
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Bake the crust for 12 to 15 minutes, until edges are beginning to brown. Remove it from the oven, and let it cool while you prepare the topping.
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To make the topping: Beat together the eggs, vanilla, sugar, salt, and baking powder.
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Gently beat in the flour, then mix in the toasted pecans and coconut.
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Spread the topping mixture over the baked crust. Return the bars to the oven, and bake for 20 to 25 minutes, until they're starting to turn golden brown.
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Remove the bars from the oven. After a couple of minutes, loosen the edges with a table knife, if necessary.
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After 5 more minutes, carefully turn the warm bars out onto a piece of parchment or foil, topping side down. Quickly cut them into squares. When they've set and are no longer fragile, place the squares, topping side up, on a rack to cool.