Make the beans: Heat a medium nonstick saute pan over medium heat. Add the chorizo and cook, breaking up the meat, until golden, about 6 minutes. Remove the chorizo to a plate lined with paper towels using a slotted spoon. Add the onion to the pan with the chorizo fat. Saute until the onion is translucent, about 4 minutes. Return the chorizo to the pan. Add the refried beans to the mixture. Continue cooking about 5 minutes; turn off the heat. Cover and keep warm.
Make the burritos: Heat the olive oil in a large heavy saute pan over medium-high heat. Add the onion and cook until translucent, about 3 minutes. Add the cauliflower and saute until tender, about 5 minutes. Season with salt and pepper. Add the oregano. Turn off the heat and set aside.
Heat a large heavy griddle over medium heat. Working in batches, heat the tortillas one at a time until they are soft and pliable, about 1 minute per side. Add 1/4 cup warm beans to the center of a tortilla, spreading it outward to the sides. Add 2 to 3 heaping tablespoons of the cauliflower mixture and 2 tablespoons of cheese. Fold in the edges and roll up to form a burrito. Return to the griddle until the cheese melts, about 10 seconds. Serve warm.