Heat the oven to 350°F. Spray an 8-inch cake pan with nonstick baking spray. Set aside.
Combine the strawberries and sugar in the bowl of a food processor fitted with the blade attachment. Puree until smooth.
Add the flour, baking powder, baking soda, salt, egg, 2/3 cup buttermilk, and vanilla. Puree until smooth. Transfer the batter to the prepared pan. Bake until the cake comes away from the side of the pan and a toothpick inserted into the center is dry, about 25 minutes.
Meanwhile, combine the confectioner’s sugar, Neufchatel, and remaining tablespoon of buttermilk in a bowl. (You can do it by hand or with a hand mixer.)
Ice the top of the cake and decorate with additional halved strawberries.