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1
Preheat oven to 325u00b0F. Line 2 rimmed, nonstick baking sheets with parchment paper or Silpats. Set aside.
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2
Sift the flour, baking powder, and salt onto a sheet of parchment paper or into a bowl. Set aside.
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3
In the bowl of a standing mixer fitted with a paddle attachment, combine the oil and 1 cup of the sugar and mix at medium speed for about 3 minutes, until fully combined. Add all of the flour mixture and mix for about 1 minute until combined. The mixture will be very thick. Transfer the batter to a separate bowl and rinse and dry the mixer bowl. It should be perfectly clean.
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4
Pour the egg whites in the mixer bowl and attach the whip. Whip at low speed for about 30 seconds, until they are foamy. Increase the speed to medium and whip, adding the sugar gradually, for about 2 minutes, or until until they hold soft peaks. Increase the speed to high and whip for 2 minutes, or until they hold stiff peaks.
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5
Remove the bowl from the mixer and fold in half of the egg whites, with a good stir to combine and lighten the batter. Then fold in the remaining egg whites gently and carefully to keep as much air in the mixture as possible.
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6
Drop the dough onto the prepared baking sheets in 2-teaspoon mounds, spacing them 2 inches apart, with 12 cookies per sheet. Bake for 10 to 12 minutes, until the cookies have spread and flattened out and are golden brown in color. Set aside to cool. Repeat with the remaining batter.
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7
While the cookies are cooling, chop the white chocolate roighly, pour the pieces into a microwave-safe container. Microwave at high power for 15 to 20 seconds, stir, microwave again for 15 to 20 seconds, stir, and repeat until the chocolate is melted. Note that microwaved chocolate does not look melted even when it is quite hot, so it must be watched carefully and stirred often to get it to the right consistency without overheating it.
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8
Assemble the cookies: When they have cooled, place them bottom-side-up (and rounded-side-down) on a work surface. Spread a thin layer of melted chocolate on each and sprinkle half of the cookies with a little shredded coconut. Top each with one of the remaining cookies, with the flat bottom side pressed gently against the filling. Pour the remaining coconut into a shallow bowl and roll the filled cookies in it to coat the sides.
