Preheat oven to 375°.
To prepare shortcakes, lightly spoon flour into dry measuring cups; level with a knife. Combine flour and next 6 ingredients (through ginger) in a large bowl, stirring with a whisk. Cut in 1/4 cup butter with a pastry blender or 2 knives until butter pieces are pea-sized. Add milk and 1/4 cup water; stir just until moist. Drop dough by level 1/4 cup measures 2 inches apart onto a baking sheet coated with cooking spray. Flatten dough to 1/2-inch thickness using lightly floured hands. Let stand 5 minutes.
Combine 1 tablespoon water and egg white. Brush egg white mixture over dough; sprinkle evenly with granulated sugar. Bake at 375° for 15 minutes or until golden. Remove from pan; cool on a wire rack.
To prepare filling, combine pears and lemon juice; toss to coat. Melt 1 tablespoon butter in a large skillet over medium-high heat. Add pear mixture; sauté 2 minutes. Stir in 3 tablespoons brown sugar; bring to a boil. Reduce heat to low; simmer for 5 minutes or until the sauce thickens slightly, stirring occasionally. Remove from heat; stir in vanilla.
Split each shortcake in half horizontally using a serrated knife. Spoon about 1/3 cup pear mixture over bottom half of each shortcake; top each serving with top of shortcake and 1/4 cup yogurt.
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.