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.