In a mixing bowl whisk together flour, baking powder, baking soda, and salt.
In another mixing bowl beat butter until light and fluffy. Add sugar and continue to beat together until fully incorporated. Scrape down side of bowl.
Add egg and vanilla and stir together.
Add flour mixture and sour cream and stir together until fully incorporated and no dry spots remain.
Line a baking sheet with parchment and using an ice cream scooper, scoop 1/4 cup sized scoops onto the prepared baking sheet, 2 inches apart (this will have to be done in batches).
Place cookies in oven and bake for 15 to 18 minutes or until cookies puff up and are barely brown around the edge.
Remove from oven and repeat until all batter has been used.
Transfer baked cookies onto a cooling rack and cool completely.
Place powdered sugar, 1/2 cup milk, corn syrup, and vanilla into a mixing bowl and stir together until a thick and smooth icing forms. Divide icing into two bowls and stir freeze dried strawberries and remaining milk into one of the bowls until fully incorporated and smooth.
Turn cookies so flat sides are up and spread half of each cookie with white icing. Place cookies into the refrigerator so icing can set, about 10 minutes. Once icing has set, spread other half of cookies with strawberry icing. Place cookies back in the refrigerator until icing has set, another 10 minutes. Serve.