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Line two cookie sheets with silicone baking mats or parchment paper.
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In the bowl of a stand mixer fitted with the paddle attachment, beat together the butter and sugars until fluffy and well-combined.
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Beat in eggs one at a time, scraping down the sides as needed.
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Stir in vanilla and almond extracts until incorporated.
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In a separate medium bowl, whisk together the flour, cornstarch, baking soda, and salt.
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Stir in flour mixture until just incorporated.
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Stir in coconut and chocolate chips until just combined.
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Cover and refrigerate dough at least 3 hours (up to 24 hours). It will hold its shape better if you refrigerate it for 8-24 hours.
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Toward the end of the chilling time, preheat oven to 350 F.
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Drop scoops of dough onto prepared cookie sheets using a medium cookie scoop (1 ½ tablespoons).
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Bake for 8-9 minutes. You want the edges to be just barely golden brown.
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Remove from oven, and let cool for 5-10 minutes on the cookie sheet.
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Transfer to wire rack to finish cooling.