Preheat oven to 400 degrees F. Bake pie crust in preheated oven for 10 to 12 minutes.

Place broccoli in a steamer over 1 inch of boiling water, and cover. Steam until tender but still firm, about 2 to 6 minutes. Drain.

Heat oil in a large skillet over medium-high heat. Saute onion, garlic and mushrooms until golden. Stir in the cooked spinach and heat through.

In a blender combine tofu, soy milk, mustard, salt, nutmeg, ground red pepper, black pepper, and parsley; process until smooth. In a large bowl combine tofu mixture with broccoli mixture. Pour into pie crust.

Bake in preheated oven for 35 to 40 minutes, or until quiche is set. Allow to stand for 5 minutes before cutting.