In a small bowl, cover the ancho chiles with boiling water. Cover; let stand until soft, 8 to 10 minutes. Drain.
Preheat the broiler. Broil the red peppers, turning occasionally, until charred all over, 10 to 15 minutes; transfer to a bowl. Cover; let cool about 15 minutes. Peel, seed and stem the peppers; place in a food processor. Add the ancho chiles.
Place the tomatoes, onion and garlic on a rimmed baking sheet lined with foil. Spray with cooking spray; season with salt and pepper. Broil until the onion softens and tomatoes char and burst, 10 to 12 minutes. Add the tomato mixture, herbs, nuts and vinegar to the processor.
Pulse until the mixture is coarsely chopped. With the machine running, stream in the EVOO and process until finely chopped; season.
Heat a cast-iron griddle or skillet over medium-high. In a medium bowl, combine the beef, onion, garlic, and herbs and spices; season with salt and pepper. Mix in the ground chorizo. Form into 6 patties (thinner in the centers for even cooking).
Drizzle the patties with oil. Cook, turning occasionally, about 8 minutes for medium. Add the cheese during the last 2 minutes of cooking; tent with foil to melt.
Top roll bottoms with lettuce, patties, romesco sauce and the roll tops.