Over a large bowl, break up the chorizo into small pieces. Add the turkey and 1/2 tsp. salt and mix well with your hands. Form into four 1/2-inch-thick patties. Press the center of each patty with 3 fingers to make an indentation to help it keep its shape during cooking.

Oil the grill grates and grill the burgers, covered, turning once, until an instant-read thermometer inserted in the center of a burger registers 165°F, about 10 minutes.

Meanwhile, in a small bowl, mash the avocado, vinegar, cumin, hot sauce, and 1/2 tsp. salt until fairly smooth.

Spread the guacamole over the bottom of each roll, top with a burger, tomato slices, and the top of the roll and serve.