In a large bowl, whisk together the flour, sugar, baking powder and salt. Using a pastry cutter, cut the butter into the flour mixture, until you have course crumbs. This can also be done with two knives or a food processor.
Whisk the eggs lightly and combine with the buttermilk. Add to the flour mixture and stir until just moist.
Place the shredded zucchini between a few layers of paper towels and squeeze to remove excess moisture.
In a small bowl, mix together the zucchini, feta, parmesan, thyme, and chives. Add this to the batter, then mix lightly. The dough will be sticky.
On a floured surface, turn the sticky dough out and knead lightly until all the cheese, zucchini and herbs are incorporated into the dough. Dust with flour, as needed, if the dough feels too wet. Roll the dough 3/4-inch thick rectangle, about 6"x9". Cut out 3-inch squares. You should have about 6 scones. Place the scones on a baking sheet lined with parchment or a silicone mat, and lightly brush with buttermilk. Sprinkle with sea salt.
Place the scones in the freezer for 30 minutes. Meanwhile, preheat the oven to 400° F.
Once the scones are chilled, bake for 20 minutes, or until golden. Sprinkle with additional parmesan cheese and serve warm.