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Preheat the oven to 350°F. Fully line the sides and bottom of an 8” square pan with parchment or a reusable pan liner.
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To make the crust: Whisk together the flour, salt, and confectioners' sugar. Work in the butter until it's evenly distributed; the mixture will be crumbly.
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Press the crust evenly and firmly into the prepared pan. If the mixture begins to stick to your hands, chill it in the freezer for 5 to 10 minutes, then continue to press. It’s important that the crust is firmly anchored to the pan without any thin spots so the filling doesn’t seep underneath.
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Bake the crust for 25 to 30 minutes, or until it's starting to brown around the edges, but is not yet pulling away from the sides of the pan. Remove it from the oven, and reduce the oven temperature to 325°F
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While the crust is baking, make the filling.
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To make the filling: In a medium bowl, combine the whole eggs, egg yolk, lime zest, and sugars, and whisk until smooth.
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Stir in the flour and salt, then the lime juice. Whisk until thoroughly combined.
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Let the filling sit for 15 minutes or so, until the bubbles (mostly) disappear.
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While the baked crust is still hot, pour the filling over it. Return the bars to the oven and bake until they appear set and relatively dry on top, about 30 minutes.
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Remove the bars from the oven and cool them on a rack. Let the bars cool completely before removing from the pan and topping.
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To make the topping: Using a small food processor or blender, pulse the freeze-dried raspberries and confectioners’ sugar together until they’re a fine powder. Use a fine-mesh strainer to sprinkle the topping over the bars before slicing and serving.
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Storage information: Bars can be kept in an air-tight container in the refrigerator for up to a week.
