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.
Remove shortcake from pan and place on a rack to cool slightly. Cut into 6 pieces and split each piece in half horizontally.
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.
Using a mixer, beat the heavy cream, sugar, vanilla, and lemon zest until soft peaks form, about 1 1/2 to 2 minutes.