To prepare shortcakes, lightly spoon flour into dry measuring cups; level with a knife.
Place flour and next 5 ingredients (through 1/4 teaspoon salt) in a food processor; pulse 2 to 3 times to combine.
Add chilled butter; pulse 10 times or until mixture resembles coarse meal. With processor on, slowly add 6 tablespoons ice water through food chute, processing just until combined (do not form a ball).
Turn dough out onto a lightly floured surface; knead lightly 4 times with floured hands.
Pat the dough into a 14 x 4-inch rectangle on a large baking sheet lined with parchment paper.
Cut dough into 8 even portions, cutting into, but not through, the dough. Brush the dough with egg white; sprinkle evenly with 2 teaspoons sugar.
Bake at 375° for 15 minutes or until golden. Remove from pan; cool on a wire rack.
To prepare filling, melt 2 teaspoons butter in a large nonstick skillet over medium-high heat.
Add apple, tossing to coat; sauté 4 minutes or until lightly browned.
Stir in brown sugar; sauté 2 minutes. Stir in the cranberries, juice, 1/4 cup water, and dash of salt.
Reduce heat to low; simmer 5 minutes or until cranberries pop, stirring frequently.
Place whipped topping and 1/8 teaspoon cinnamon in a small bowl, and fold gently to combine. Place shortcake on a cutting board or work surface.
Carefully split shortcake in half horizontally using a serrated knife. Place bottom half of shortcake on a platter; spread evenly with about 1/2 cup whipped topping mixture and apple mixture; top with shortcake top.
Cut along score lines with a serrated knife to form 8 portions. Top each portion with 1 tablespoon remaining whipped topping mixture.
When mixing the dough for shortcakes, use a light hand and work quickly for the most tender cakes. If the recipe calls for kneading the dough, knead lightly only a few times so the dough doesn't become overworked.
Use a serrated knife to split the shortcakes. It will cut through the cakes without crumbling them.
You can bake the shortcakes up to a day ahead. Cool completely, and store at room temperature in a large zip-top plastic bag. To reheat, wrap in foil and heat at 350° for 10 minutes.
To freeze shortcakes, cool them completely, place in a heavy-duty zip-top plastic bag, and freeze up to two months. Thaw at room temperature, then reheat as instructed above.