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Whisk together the oats, flours, baking soda and salt. Set aside.
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Beat the butter with the lime zest. Add the sugars and beat until fluffy. Scrape the sides and bottom of the bowl as needed.
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Add the eggs, one at a time, beating to incorporate. Beat in the lime juice and vanilla.
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Add the whisked flour-oat mixture and mix in on low speed.
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Add the white chocolate and flaked coconut and mix in.
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Cover with plastic wrap and chill for at least 2 hours and preferably overnight. You can also chill for up to 4 days.
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Preheat the oven to 350 F when you are ready to bake.
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Using an ice cream scoop, scoop out 2-tablespoon portions onto a baking sheet 2 inches apart (I like 6 to a cookie sheet). Sprinkle with vanilla salt. Bake for 12-14 minutes, until golden at the edges but still a little soft in the center.
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Let cool for 5 minutes on the baking sheet before transferring to a cooling rack.