Combine sliced strawberries and basil simple syrup in a bowl and set aside.
For the shortcakes, combine flour, 3 Tbsp. sugar, baking powder, and salt in a food processor. Add butter pieces and process until the mixture resembles cornmeal. Transfer to a bowl.
Blend half & half with the beaten egg and pour into bowl with the flour mixture. Add fresh basil. Stir until large clumps form; continue mixing and kneading on a lightly floured countertop. *Add flour as necessary until dough is the right consistency.
Pat the dough into a 9x6 inch rectangle about 1 inch thick. Use a floured 2 3/4 inch biscuit cutter or the top of a glass to cut out 8-12 circles (depending on size). Place each dough circle on a parchment-lined baking sheet, brush with beaten egg white, and sprinkle with remaining 2 Tbsp. sugar.
Bake until golden brown, 12-14 minutes.
Prepare whipped cream by combining whipping cream and 2 Tbsp. sugar in a medium mixing bowl. Mix and low speed to dissolve sugar, then at high speed until mixture is light and fluffy and has doubled in volume.