Place the zucchini in a colander and sprinkle with ½ tsp salt. Thoroughly mix salt into zucchini with your hands. Let sit for 10 minutes. Grate the cheese.
Preheat oven to 350 F and set rack to middle position. Butter a 9 - 10 inch pie plate or quiche dish.
Rinse the zucchini with running water very thoroughly. With clean hands, squeeze out as much liquid from the zucchini as you can. Place the zucchini into a medium bowl and mix well with the dried dill and chives.
Measure salt, pepper, eggs and heavy cream into a medium bowl and beat until frothy.
Layer ¼ of the cheese into the pie plate followed with ⅓ of the zucchini. Alternate layering cheese and zucchini until used up. Gently pour the egg mixture over the quiche.
Bake for 40-50 minutes depending on you oven or until the quiche is browned and just slightly soft in the middle. Remove from the oven and let cool to room temperature before serving.
Cover with cling film and refrigerate any leftovers. Reheat in the microwave or oven. Great served with a green salad.
Serve warm with a green salad. Serves 6 at 4.1g NET CARBS per serving.