Line a baking sheet with parchment paper. In a large bowl, whisk together the flour, baking powder, baking soda, salt, brown sugar, cinnamon, nutmeg, and ginger.
3 cups All-purpose flour, 2 tsp Baking powder, 1/2 tsp Baking soda, 1 1/2 tsp Ground cinnamon, 1/2 tsp Ground nutmeg, 1/2 tsp Ground ginger, 1/2 tsp Kosher salt, 1/3 cup Dark brown sugar
Add the frozen shredded butter and toss to coat, gently breaking up any large clumps. Add the grated carrots and nuts, tossing to distribute evenly.
1/2 cup Unsalted butter, 1 cup Finely grated carrots, 1/2 cup Chopped pecans
Make a well in the center. Pour in the cold heavy cream, beaten egg, and vanilla. Mix gently, bringing in the dry ingredients a little at a time until a shaggy dough forms.
1 1/4 cup Heavy cream, 1 large Egg, 1 1/2 tsp Vanilla extract
Turn the dough out onto a lightly floured surface. Gently press the dough into a 1-inch thick circle (about 7"x7"). Cut into 8 wedges, place them on the prepared baking sheet, and freeze for 15 minutes. Preheat the oven to 375ºF.
Brush the tops with heavy cream, and sprinkle with coarse sugar if desired. Bake for 18-20 minutes, until set and golden brown around the edges. Cool on a wire rack for at least 20 minutes before adding the glaze.