FOR THE STRAWBERRIES:

1. Mix crushed and quartered berries with lilac sugar in medium bowl; set aside while preparing shortcakes (or up to 2 hours)

FOR THE SHORTCAKES:

1. Adjust oven rack to lower middle position; heat oven to 200c/400f degrees.
2. Mix flour, salt, baking powder, and 3 tablespoons lilac sugar in medium bowl.
3. Using large holes of box grater, grate butter into the dry ingredients. Toss butter with flour to coat. Use pastry cutter (or a fork) to finish cutting butter into the flour. Or scoop up coated butter with both hands, then quickly rub butter into dry ingredients with fingertips until most of butter pieces are the size of split peas.
4. Mix beaten egg with 1/4 cup Greek yogurt & 1/4 cup milk; pour into flour mixture. Toss with fork until large clumps form. Turn mixture onto floured work surface and lightly knead until it comes together.
5. Pat dough into 9- by 6-inch rectangle, 3/4 inch thick. Flour a 2 3/4-inch biscuit cutter (I used a similar sized cup); cut 6 dough rounds. Place rounds 1 inch apart on small baking sheet lined with parchment; brush dough tops with heavy cream and sprinkle with remaining 2 tbsp lilac sugar. (Can be covered and refrigerated up to 2 hours before baking.)
6. Bake until golden brown, 12 to 14 minutes. Place baking sheet on wire rack; cool cakes until warm, about 10 minutes.

FOR THE GREEK YOGURT WHIPPED CREAM:

1. Chill a non-reactive, deep bowl and beaters mixer in freezer for at least 20 minutes.
2. Add cream and lilac sugar to the chilled bowl; beat on low speed until small bubbles form, about 30 seconds. Increase speed to medium; continue beating until beaters leave a trail, about 30 seconds more. Increase speed to high; continue beating until cream is smooth, thick, and nearly doubled in volume, about 20 seconds for soft peaks.
3. Add in the Greek yogurt and whip for another ten seconds or so, until whipped cream is thick. If necessary, finish beating by hand to adjust consistency.

TO SERVE:

1. Split each cake crosswise by hand (I used a fork to help split the cake in half); spoon a portion of berries and then a dollop of whipped cream over each cake bottom. Cap with cake top; serve immediately.