Mix the zucchini with 1/4 tsp of salt. Place in a colander to drain for 30 minutes. Squeeze the zucchini to get as much of the water out as possible. Place between paper towels until ready to use.
Preheat the oven to 400 degrees. Combine flours, salt, pepper, baking powder and soda. Cut the butter into the flour mix until no large chunks are visible.
Mix the zucchini, and herbs into the flour mixture.
Add the egg and the buttermilk. Mix until just combined.
On a floured surface roll the dough out to 1/4 inch thick square. Cut the dough into 3 equal parts.
Crumble the goat cheese on one portion of the dough. Top the goat cheese with the second strip of dough. Crumble more goat cheese on the dough and stack the last strip of dough on top. Gently roll the dough to 1 1/2 inch thickness.
Cut the dough into 8 equal squares and place on a lined baking sheet. Brush the tops with egg wash. Bake in a 400 degree oven for 15-20 minutes.