Crush 3 cup strawberries with a potato masher. Slice remaining berries and stir into crushed berries with ⅓ cup sugar. Let sit at room temperature, stirring occasionally until fruit begins to release its juices, about 30 minutes or up to 2 hours.

Preheat oven to 425 degrees. Pulse flour, 3 tablespoons sugar, baking powder, and salt in food processor until combined. Scatter butter pieces over top and pulse until mixture resembles coarse cornmeal, about 15 pulses. (Don't over mix.) Transfer to a large bowl.

In a separate bowl, whisk half-and-half and egg together. Add half-and-half mixture to flour mixture and stir with rubber spatula until large clumps form. Turn mixture onto lightly floured counter and knead lightly until dough comes together.

Using your fingertips, pat dough into a 9 by 6-inch rectangle about 1 inch thick. Cut out 6 biscuits using floured 2 ¾-inch biscuit cutter. Pat remaining dough into 1-inch thick piece and cut out 2 more biscuits. Place biscuits on parchment-lined baking sheet spaced 1 inch apart.

Brush top of biscuits with egg white and sprinkle with coarse sugar. Bake biscuits until golden brown, 12 to 14 minutes. Let biscuits cool on baking sheet for about 10 minutes.

Split each biscuit in half and place bottoms on individual serving plates. Spoon strawberry topping over each bottom, then top with a dollop of whipped cream. Cap with biscuits tops and serve immediately.