In a large bowl, whisk together the flour, baking powder, sugar, salt, and cinnamon.
Cube the butter into 1 cm thick pieces, add to the flour mixture. Toss with your hands to coat in the flour, then squeeze the pieces into flatter pieces, breaking them up with your hands until they are all about bean sized and combined into the flour. Make a well in the center.
Pour the buttermilk into the center of the well, then add the carrots. Working quickly, use your hands to form a shaggy dough. Give it a few kneads in the bowl to bring it together, then put the bowl in the refrigerator. Let chill for 30 minutes.
Preheat the oven to 400°F. Whisk together the egg in a small bowl.
Flip the dough out onto the counter and flatten into a rectangle. Cut the dough into thirds and place them on top of each other, press down to create numerous flakey layers. Rotate this new piece of dough 90° and repeat one more time. Then pat the dough down into a rectangle about 2" tall. Cut into 6 even pieces.
Evenly spread out the biscuits on a parchment lined baking sheet. Brush each with the egg wash.
Bake for 24-26 minutes, or until the biscuits are golden and almost double in height. Serve warm!