Add ground beef and chorizo to a large bowl, and, using two forks, fluff the meat (see note above) to evenly mix and lighten the texture. Mix in garlic powder, kosher salt and black pepper, then the cheese. Form the meat mixture into 4 even patties.
Preheat a gas or charcoal grill over medium-high heat. Brush the burgers lightly with vegetable oil. Also brush the grill grates with vegetable to keep the patties from sticking. Grill the patties directly over the heat for about 4 - 6 minutes a side or until cooked through. Let rest for a few minutes before building the burger. I like to cook the burgers to 155°F, and the temp goes up to 160°F as they rest. I've also cooked these burgers under the broiler (about 7 minutes per side) and using a panini press fitted with flat plates (6 minutes total).
Stack up the burger as follows: bottom bun, mayo, burger patty, tomato slice, lettuce, ketchup, top bun. Enjoy immediately!