1
Separate the strawberries, in an equal arrangement. Put the first set of strawberries in a food processor and pulse in short bursts just until they are chopped into small pieces (about four or five pulses should do it), and set it aside. Be careful not to puree them.
2
Sift flour, baking powder, baking soda, and salt into a medium bowl, and set aside.
3)Put brown sugar and oil in a large bowl and mix well, using the back of a spoon to break up any lumps of sugar. Whisk in chopped strawberries and yogurt until combined, then whisk in eggs, one at a time, just until combined. Fold in flour mixture in two parts, being careful not to overwork the batter. Cover and refrigerate for 30 minutes.
4
Preheat in oven to 350 degrees. Using a measuring spoon, drop a heaping tablespoon of batter onto a parchment-paper-lined baking sheet to form each cookie, spacing dollops about two inches apart. Working in batches, bake until cookies are set, which will take ten to twelve minutes. Remove cookies from the oven, and cool completely.
5
Take the other set of strawberries and puree these, then set aside. Whisk egg whites and granulated sugar together in the top of a double boiler until sugar is dissolved and mixture is milky white which takes about two minutes.
6)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 two minutes. Remove whisk attachment and replace with a paddle attachment next. Add butter and beat until smooth and fluffy, and this should take five minutes give or take.
7)Add strawberry puree and beat again until well combined. After a minute you're ready to go.
8
Generously frost the flat side of half of the cookies, then top each with an unfrosted cookie to form sandwiches. Transfer to a platter and serve.