1. Preheat oven to 425°. Mix together first 5 ingredients and 1/3 cup sugar. Add butter, and process in food processor until mixture resembles coarse meal. Add carrot and ginger, and pulse just until blended.
2. Whisk together egg, buttermilk, and vanilla in a separate bowl until blended. Add to flour mixture, and pulse just until blended and slightly moist. (Dough will be sticky.)
3. Transfer dough to a well-floured surface with well-floured hands. Divide in half, and pat each half into a 3/4-inch-thick circle. With a floured knife, cut each circle into 6 wedges.
4. Place wedges on a lightly greased baking sheet. Brush top of each scone with egg wash, and sprinkle each with 1/4 teaspoon sugar.
5. Bake at 425° for 15 minutes or until golden. Serve warm, or let cool completely, and store up to 2 days in an airtight container at room temperature.