Add the all-purpose flour, salt, and sugar to a food processor and mix until completely combined. Next, add the coconut oil and process until the texture is crumbly. Finally, add the water and process into a dough. The texture should be moist and flexible.
Dust the countertop or a large cutting board with flour. Place the ball of dough on top of the flour-coated surface. Roll it out into a giant round that can fit over your 9-inch pie dish.
Carefully lift the dough, placing it over the pie dish. Press and tuck it along the sides and remove any excess dough hanging over the sides of the dish. Place the pie crust into the fridge to chill.
Drain and press the tofu to remove excess water while you are prepping the vegetables. Wash and chop the vegetables accordingly. When this step is completed, preheat the oven to 350°F/180°C.
Add the tofu, cornstarch, nutritional yeast, turmeric, onion powder, garlic powder, and salt into the food processor, processing until well mixed (about 1 minute). Add the almond milk and process again (for about 20 seconds) until it reaches a smooth consistency. Set aside.
Add the olive oil to a pot along with the chopped onion and crushed garlic and sauté on medium heat until the onions are softened and translucent. Add the mushrooms and peppers to sauté with the onions until the mushrooms are softened. Finally, add the chopped baby spinach and parsley, sautéing until just wilted.
Layer the filling on top of the prepared pie crust and smooth it down evenly. Place it into the oven and bake uncovered for 40 minutes until firm and golden on top.
When the quiche is cooked, remove it from the oven and allow it to cool for 10 minutes before slicing and serving. Serve warm or chilled.