Preheat oven to 200C. Mix flour,salt,baking powder and 3 tablespoons castor sugar in a bowl. Add butter to dry ingredients and use your fingertips to crumble butter into flour. Whisk egg into cream,and pour into flour mixture a little at a time,using a fork to mix. You may not need all the eggy cream to make the dough come together,so add it carefully.
When dough comes together,turn it out onto a lightly floured surface,and roll gently to a thickness of about 2 centimetres. Dip a 6.5-centimetre round cutter in flour and cut out as many rounds as you can. Work scraps back into a dough,reroll and finish cutting out - you should get 8 rounds.
Place shortcakes about 2.5 centimetres apart on a greased or lined baking sheet,brush tops with egg white and sprinkle with 2 tablespoons castor sugar. You can cover and refrigerate them now for up to 2 hours before baking.
When ready,bake for 10-15 minutes,until golden-brown,and let them cool briefly on a wire rack.
Meanwhile,crush half the strawberries with the remaining 1 tablespoon sugar,add balsamic vinegar if using,and halve or quarter the remaining strawberries,depending on their size.
The shortcakes should be eaten while still warm,so split each one across the middle,cover with a spoonful of the crushed strawberry mixture,add a few halved or quartered strawberries,then dollop some whipped cream or creme fraiche on top,and put the top back on.
Serves 8