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Mix strawberries with 3 tablespoons sugar and refrigerate while juices develop, at least 30 minutes. Preheat the oven to 400 degrees F. Sift together the flour, baking powder, baking soda, remaining 2 tablespoons sugar, and salt in a medium bowl. Add heavy cream and mix until just combined. Place mixture in an ungreased 8-inch square pan and bake until golden, 18 to 20 minutes.
Spoon some of the strawberries with their juice onto each shortcake bottom. Top with a generous dollop of whipped cream and then the shortcake top. Spoon more strawberries over the top and serve.