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Preheat the oven to 350*F. Line a baking sheet with parchment paper.
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Cream the butter and both sugars in the bowl of a stand mixer with a whisk attachment on medium speed until light and fluffy, about 3-5 minutes, scrapping down the sides of the bowl as needed.
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While it's creaming, mix together the flour and salt in a small bowl. Stir the chopped pecans into the flour mixture.
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Once the butter and sugar is light and fluffy, mix in the vanilla until it is completely combined. Add half the flour mix and beat on low until just combined. Scrap down the sides of the bowl and add the rest of the flour and mix again on low until just combined.
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Using a tablespoon, scoop out the dough. Shape each bit of dough you scoop out into about a two inch log, then gently bend the little logs into the crescent moon shape and place on your prepared baking sheet. Work quickly because if the butter gets too warm, the cookies will spread and you won't have the nice defined crescent shape!
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Bake for 17-20 minutes, until golden brown around the edges. Remove from the oven and let cool on the baking tray for ten minutes. Remove from baking tray and let cool completely on cooling rack. Once totally cool, put the cup of powdered sugar in a shallow bowl and coat the cookies gently in the sugar.
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Store in an airtight container for a week or more.