Preheat the grill to 375°F or cast iron skillet to medium-high.
In a large mixing bowl, combine the chorizo, ground beef, Worcestershire sauce, salt, and pepper.
Divide the mixture into 4 equal portions. Roll each portion into a ball, then use the palm of your hand to flatten each ball into a patty of about 1/2-inch thickness.
Place the burger patties over the direct heat side of your preheated grill. Grill for about 7 minutes per side, or until internal temperature reaches 160°F.
While burgers are still on the grill, top each burger with a slice of cheese then close the grill for 1-2 minutes, just long enough for the cheese to melt.
Place your buns face-side down on the direct heat of your grill and toast for 1-2 minutes. Place cooked burgers on the toasted buns, top with guacamole, if using, and serve.