Heat oven to 425°F (220°C). Line a baking sheet with parchment paper.
In a large mixing bowl, stir together 2 cups all-purpose flour, 1/3 cup granulated sugar, 1 tablespoon baking powder,1/4 teaspoon salt, 1 teaspoon ground cinnamon, 1/4 teaspoon ground nutmeg, and 1/4 teaspoon ground allspice.
Grate 1/2 cup cold butter using a cheese grater and stir into the flour mixture OR cut butter into small pieces and use a pastry cutter to cut the fat into the flour mixture until it resembles coarse meal or sand.
Stir in 1 cup heavy cream, 1/2 cup finely shredded carrots, and finely chopped 1/2 cup chopped walnuts until it just comes together.
Turn the dough onto a clean countertop and form it into a ball. Press into a 2-inch thick circle. Using a knife, cut into 8 wedges.
Place scones on the prepared baking sheet. Bake for 13–15 minutes, or until the tops are golden brown.
While the scones are baking make the glaze by whisking 1/2 cup powdered sugar and 1 teaspoon ground cinnamon together with 2 tablespoons milk, and 1 teaspoon vanilla extract in a small bowl.
Remove the scones from the oven and transfer to a wire cooling rack. Drizzle with glaze and let cool before serving.