Prepare cremini mushrooms by mincing them as finely as you can. The finer you can mince the mushrooms, the better it will be for your burgers later. Combine the minced mushrooms in a large mixing bowl with raw, ground chorizo. Use your hands to blend the ingredients together, and you can add any additional spices at your discretion.
Heat the olive oil in a wide pan over medium-high heat. Portion the chorizo burger mixture and roll the portions into balls, packing the meat tightly with your hands. When the pan is hot, press the burgers down in the pan until they spread into thick patties. Let the burgers cook undisturbed on one side until they get a good char – you want the burgers well done. Place a lid over your pan to trap the heat and stop any grease from splattering.
Flip the burgers over with a spatula and reduce the heat slightly on your stove. Place a slice of pepper jack cheese over each burger, and let the burgers finish cooking. The melted cheese will also help ensure the burger stays together when it’s done. Serve a chorizo cheeseburger with your favorite burger toppings, such as lettuce, tomato, or avocado.