Preheat oven to 450 degrees F. Line a large baking sheet with foil and spray lightly with nonstick cooking spray. In a large mixing bowl toss together the cauliflower florets with a liberal tablespoon of olive oil and sprinkle with the cumin, chili powder, turmeric and salt. Mix again and carefully transfer the spice-covered cauliflower to the prepared baking sheet, spreading it into a single layer. Bake for approximately 25-30 minutes.
As the cauliflower is baking, cook the quinoa according to package instructions (and with just 1 cup if water- this will help prevent the quinoa from being soggy).
In a separate larger bowl, whisk together the eggs and add the shredded cheese with the breadcrumbs. Mix to combine and set aside.
Remove cauliflower from the oven and set aside to cool, approximately 5 minutes. Transfer cauliflower to the bowl of a large food processor and pulse until finely chopped, but not pureed (think micro-florets).
Transfer cooked quinoa and cauliflower to the large mixing bowl containing the eggs, breadcrumbs and cheese. Mix well (I used my hands). With clean hands, roll the mixture into approximately 8 even balls. Cup each ball in your hands and squeeze tightly, rotating the ball as you squeeze. Gently and slowly press the ball into a disc. Transfer each patty to a plate, covering tightly with plastic wrap, and refrigerating for at least 30 minutes if possible.
As the veggie patties set, prepare the chipotle mayo. In the bowl of a small food processor or blender, add all ingredients for the chipotle mayo. Blend until smooth. Season to taste, adding more chipotle chilies for a hotter sauce.
When ready to eat, add 1-2 tablespoons of oil to a large skillet over medium high heat. When pan is hot and oil is shimmering, carefully transfer patties to skillet and cook for approximately 4-5 minutes on each side (you want a golden outside). Avoid temptation to crowd the pan. While cooking, use your spatula to gently push the sides of the patty to form a disc.
Transfer patties to toasted buns and top with avocado, veggies and chipotle mayo.