Preheat oven to 400 degrees Fahrenheit. Grease a 10-inch cast iron skillet or large tart pan with cooking spray. In a mixing bowl, stir together the almond meal, garlic, thyme, salt and pepper. Pour in the olive oil and water and stir until the mixture is thoroughly combined.Press the dough into your prepared skillet/pan until it is evenly dispersed across the bottom and up the sides (if you are using a cast iron skillet, make sure the dough goes at least 1¼ inch up the sides). Bake until the crust is lightly golden and firm to the touch, about 18 to 20 minutes.In a large skillet over medium heat, warm enough olive oil to lightly coat the pan. Cook the mushrooms with a dash of salt, stirring often, until tender. Toss in the arugula and let it wilt, while stirring, about 30 seconds. Transfer the mixture to a plate to cool.In a mixing bowl, whisk together the eggs, milk, salt and red pepper. Stir in the goat cheese and the slightly cooled mushroom and arugula mixture.Once the crust is done baking, pour in the egg mixture and bake for 30 minutes, or until the center is firm to the touch and cooked through. Let the quiche cool for 5 to 10 minutes before slicing with a sharp knife. Serve immediately.