Cut the cauliflower in half and break it into small florets.
Place the florets in a food processor and pulse until they break down to rice-size pieces. Remove from the processor and set aside.
Add the mushrooms to the food processor and pulse until broken down to rice-size pieces.
Heat the olive oil in a large skillet over medium heat. Add the onion and garlic to the pan and cook for about 4 minutes, until fragrant and the onion is translucent.
Add the cauliflower, mushrooms, cumin, smoked paprika, chili powder, soy sauce, salt, and pepper and stir. Cook for about 10 minutes, until the cauliflower and mushroom mixture is tender and the water released from the mushrooms has evaporated.
Heat a tortilla over low heat in a large, greased skillet.
Sprinkle the tortilla with a layer of cheese, then add a layer of cauliflower “meat”, caramelized onions and peppers, and another layer of cheese.
Top with another tortilla and cook for about 4 minutes, until the bottom layer of cheese has melted and the bottom tortilla is golden brown.
Carefully flip the quesadilla and cook for another 4 minutes, until all of the cheese has melted.