Preheat your oven to 400°F (200°C) and line a baking sheet with parchment paper.

Chill the cold butter by slicing it into small cubes and placing them in the freezer for 15 minutes.

In a small bowl, combine the egg yolk, a splash of vanilla extract, and heavy cream. Refrigerate.

In a large mixing bowl, whisk together flour, brown sugar, granulated sugar, baking powder, cinnamon, ginger, nutmeg, and salt. Add the chilled butter, mixing until the texture resembles coarse crumbs.

Stir in the grated carrots and any optional nuts. Add the chilled wet mixture and fold until just combined.

Turn the dough onto a floured surface and pat it into a circle about 1-inch thick. Cut into triangular wedges.

Place the shaped scones on the baking sheet, cover with plastic wrap, and chill in the refrigerator for at least 15 minutes.

Brush the tops with heavy cream and bake for 18 to 22 minutes until golden brown.

Cool the scones on a wire rack. Beat together cream cheese and butter until smooth, then mix in vanilla and powdered sugar for the glaze.

Drizzle the cream cheese glaze over the cooled scones and serve warm.