Preheat your oven to 425°F and adjust the oven rack to a lower-middle position.

Combine flour, salt, baking powder, and 3 tablespoons sugar in a medium bowl. Grate 2 tablespoons of frozen butter into the dry ingredients and toss to coat. Repeat with the remaining butter.

Combine the egg and half-and-half, then pour it into the dry ingredients. Toss with a fork to form dough clumps. Press clumps into a ball, adding a bit more half-and-half if necessary to bring the dough together.

Turn the dough onto a work surface and press it into an 8x4-inch rectangle. Cut into 6 squares and place them about 1-inch apart on a baking sheet. Brush tops with egg white (optional) and sprinkle with 2 tablespoons sugar. Bake until golden brown, about 12-14 minutes. Let cool for 5-10 minutes.

To prepare the berry mixture, combine thawed and fresh berries with sugar in a bowl and let stand until dissolved.

For whipped cream, beat chilled heavy cream to soft peaks using a hand mixer. Gradually add 1 tablespoon sugar and vanilla extract while beating.