Preheat oven to 375˚ F.
Combine flour, sugar, baking powder, baking soda, and salt in a food processor bowl with steel blade and blend for 8 seconds.
Add finely chopped eggs and pulse 10 to 12 times to incorporate.
Cut butter into flour mixture by pulsing 8 to 10 times, just until mixture resembles a coarse meal. Do not over mix.
Add milk to mixture gradually or through small liquid feed on the food processor. Pulse just until dough begins to clump together.
Turn dough onto a lightly floured surface. Pat into 8-inch circle, approximately ½ to ¾ inch thick. Cut into 8 wedges or pat into a more oblong shape and cut with 3-inch round biscuit cutter.
Place on parchment lined or buttered baking sheet. Brush tops of shortcakes with milk and sprinkle with sugar if desired.
Bake 12 to 15 minutes or until golden brown. Cool slightly.
Combine fresh strawberries, sugar and balsamic vinegar. Let stand at room temperature for about 30 minutes, stirring occasionally.
Split shortcakes lengthwise, fill and top with sweetened sliced strawberries, and garnish with a dollop of whipped cream.