Preheat oven to 400F. Line a large sheet pan with parchment paper and set aside.
Place shredded carrot in the center of a kitchen towel. Tightly squeeze to drain water out of carrot. Set aside.
In a large bowl, combine flour, both sugars, spices, baking powder, and salt. Use a pastry cutter or your fingers to work frozen shredded butter into flour mixture until crumbly.
In a medium bowl, whisk egg, 1/4 cup heavy cream, milk, and vanilla until smooth. Pour liquid mixture, shredded carrots, and pecans over flour mixture and gently fold until a shaggy dough forms. Turn dough out onto a surface and gently knead several times until dough comes together.
Lightly flour surface and pat dough into a 1-inch thick circle. Cut circle into 4 wedges using a benchscraper or knife and stack the pieces on top of one another. Use your hands to flatten dough back down to 1-inch and pat into a circle.
Cut dough circle into 8 wedges and arrange 2 inches apart on prepared sheet pan. Place pan in the freezer for 15 minutes to chill the fats in dough before baking.
Brush scones with remaining 1 tablespoon heavy cream. Bake scones at 400F 15-18 minutes until golden-brown. Allow scones to cool 10 minutes on sheet pan then transfer to a wire cooling rack to cool completely.