Preheat the oven to 375ºF. Grease a 9" pie dish and set aside.
For the filling, heat the olive oil in a large pan. Add the garlic, mushrooms, and leek and saute until softened, about 3 minutes. Remove from the heat and allow to cool for about 5 minutes.
In a large bowl, mix together the eggs, almond milk, nutritional yeast, salt, pepper, and thyme. Fold in the veggies. Set aside.
To the bowl of a food processor, add the crust ingredients. Process until a dough starts to come together. You should be able to squeeze it between your fingers and it will hold together.
Dump the "crust" into the pie dish and press it into the bottom and then up the sides. Feel free to smooth the edges over with your fingers.
Pour the filling into the crust. Place on the center rack of the oven and cook for 30 minutes.
Remove from the oven and allow to cool for a few minutes. Sprinkle with a bit more fresh thyme, slice and serve.