In a large bowl, whisk together flour, baking powder, sugar, and salt.
Cut the butter into the flour mixture with a pastry cutter or fork, until it resembles gravel.
In a separate bowl, whisk together two of the eggs and the buttermilk. POur it into the flour mixture and whisk to combine.
Add carrots, zucchini, bell pepper, and cheddar. Stir to combine.
Turn the dough out on a lightly floured surface and knead a few times, just to bring it all together. Use your hands to form a circle with the dough, about ¾” thick. Cut into 8 wedges.
Line a baking sheet with parchment paper. Set the slices on the baking sheet.
Mix together the last egg and about 1 tablespoon of water. Brush this egg wash onto the tops of the scones.
Bake for 20-22 minutes, until the tops are golden.