To prepare the crust, mix together flour, salt and baking soda in a bowl, then add 6 Tbsp of 1 Tbsp-sized pads of chilled butter to the bowl. Work the butter into the flour mixture using a dough blender or a fork until the butter is in small crumbles. Next, add 1 Tbsp cold water to the mixture at a time, while continuing to work the dough together with the dough blender. You're done mixing once the dough can be formed into a ball with only small flecks of unmixed butter visible.
Preheat your oven to 400º F. Using about 1 tsp of butter, grease the inside of your quiche pan. Next, add your crust dough to the dish and, using your fingers, evenly spread along the bottom and the sides of the dish. Once evenly spread, lightly poke the dough with a fork a dozen or so times on the bottom of the dish.
Grate your zucchini and then, using a cheesecloth or your hands, strain out as much of the water as you can and then add 1 1/2 C to a small bowl.
Next, chop your chives and shred your cheddar and add it to the bowl with the zucchini. Mix together until evenly combined and then add the zucchini mixture to your quiche dish, evenly spreading it out over the dough.
In a bowl, beat together the eggs, heavy cream, salt, and pepper and then gently pour the egg mixture over the zucchini in the quiche dish.
Cut tomatoes into thin slices and arrange them in a pretty pattern over the top of the quiche. It's best to use a lower-moisture tomato like romas, or to seed a high-moisture variety first.
Bake in a preheated oven at 400º F for 35-40 minutes or until golden brown and the center of the quiche has set.