Preheat oven to 400 degrees.
Grease pan 9 or 10-inch quiche pan or pie plate with olive oil.
Place sweet potato chunks and oats into a food processor. Pulse until finely chopped, like the consistency of rice. Add the egg and ½ teaspoon salt and pulse until the mixture is well combined and has a thick consistency.
Spread mixture evenly onto the bottom of the prepared pan, and a little on the sides. Bake for 25-30 minutes until set and a little dry to the touch. Set aside. Reduce oven temperature to 350 degrees.
While crust is baking, prepare the vegetable filling. Warm olive oil in a large skillet over medium heat. Add the sliced leek and shallot. Sauté until tender and translucent, about 5-7 minutes.
Add the mushrooms, garlic, turmeric, cayenne pepper, and ¾ teaspoon salt. Continue to sauté for another 5-6 minutes or until the mushrooms have softened. Stir in spinach and remove from heat.
In a medium bowl, beat together eggs and coconut milk. Add the cooked vegetables to the egg mixture. Pour into the cooked pie crust and dot with goat cheese on top, if using. Bake (reminder: at 350 degrees) for 30-40 minutes or until the center is set and springy. Serve warm or at room temperature.