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1
To make cookies: Put strawberries in a food processor and pulse in short bursts just until they are chopped into small pieces (about 4 to 5 pulses), and set aside.
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2
(Be careful not to puree them.)
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3
Sift flour, baking powder, baking soda, and salt into a medium bowl, and set aside.
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4
Put brown sugar and oil in a large bowl and mix well, using the back of a spoon to break up any lumps in sugar.
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5
Whisk in chopped strawberries and yogurt until combined, then whisk in eggs, one at a time, just until combined.
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6
Fold in flour mixture in two parts, being careful not to overwork the batter.
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7
Cover and refrigerate for 30 minutes.
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8
Preheat oven to 350 degrees.
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9
Using a measuring spoon, drop a heaping tablespoon of batter onto a parchment-paper-lined baking sheet to form each cookie, spacing dollops about 2 inches apart.
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10
Working in batches, bake until cookies are set and a toothpick inserted in the middle comes out clean, 10 to 12 minutes.
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11
Remove cookies from oven; cool completely.
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12
To make filling: Puree strawberries in a food processor until smooth (about 15 seconds); set aside.
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13
Whisk egg whites and granulated sugar together in the top of a double boiler until sugar is dissolved and mixture is milky white, about 2 minutes.
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14
Transfer egg white mixture to the bowl of an electric mixer fitted with a whisk attachment and whisk on high speed until soft peaks form and mixture is glossy, about 2 minutes.
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15
Remove whisk attachment and replace with paddle attachment.
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16
Add butter and beat until smooth and fluffy, about 5 minutes.
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17
Add reserved strawberry puree and about 3 to 5 drops food coloring (frosting should be a light shade of pink), and beat again until well combined, about 1 minute more.
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18
To assemble: Generously frost the flat side of half of the cookies, then top each with an unfrosted cookie to form sandwiches.
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19
Transfer to a platter and serve.
